Libor Snobl's page

My papers, preprints and other research works:
• M.F. Hoque, O. Kubu, A. Marchesiello and L. Snobl, New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases, Eur. Phys. J. Plus (2023) 138: 845 [arXiv:2309.12718].
• O. Kubu and L. Snobl, Cylindrical first-order superintegrability with complex magnetic fields, J. Math. Phys. 64 (2023) 062101 [arXiv:2212.04141].
• M.F. Hoque and L. Snobl, Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields, J. Phys. A: Math. Theor. 56 (2023) 165203 [arXiv:2212.05338].
• O. Kubu, A. Marchesiello and L. Snobl, New classes of quadratically integrable systems in magnetic fields: The generalized cylindrical and spherical cases, Ann. Phys. 451 (2023) 169264 arXiv:2206.15305.
• A. Marchesiello and L. Snobl, Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion, J. Phys. A: Math. Theor. 55 (2022) 145203.
• O. Kubu, A. Marchesiello and L. Snobl, Superintegrability of separable systems with magnetic field: the cylindrical case, J. Phys. A: Math. Theor. 54 (2021) 425204.
• S. Bertrand, O. Kubu and L. Snobl, On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields, J. Phys. A: Math. Theor. 54 (2021) 015201 [arXiv:2008.01987].
• F. Fournier, L. Snobl and P. Winternitz, Cylindrical type integrable classical systems in a magnetic field, J. Phys. A: Math. Theor. 53 (2020) 085203 [arXiv:1909.05307].
• A. Marchesiello and L. Snobl, Classical Superintegrable Systems in a Magnetic Field that Separate in Cartesian Coordinates, SIGMA 16 (2018), 015, 35 pages [arXiv:1911.01180].
• S. Bertrand and L. Snobl, On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals, J. Phys. A: Math. Theor. 52 (2019) 195201 [arXiv:1812.09399].
• O. Kubu and L. Snobl, Superintegrability and time-dependent integrals, Archivum Mathematicum 55 (2019) 5, pp. 309-318.
• A. Marchesiello, L. Snobl and P. Winternitz, Spherical type integrable classical systems in a magnetic field, J. Phys. A: Math. Theor. 51 (2018) 135205.
• A. Marchesiello and L. Snobl, An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals, SIGMA 14 (2018), 092, 11 pages [arXiv:1804.0303].
• A. Marchesiello and L. Snobl, Superintegrable 3D systems in a magnetic field corresponding to Cartesian separation of variables, J. Phys. A: Math. Theor. 50 (2017) 245202 .
• A. Marchesiello, L. Snobl and P. Winternitz, Three-dimensional superintegrable systems in a static electromagnetic field, J. Phys. A: Math. Theor. 48 (2015) 395206 [arXiv:1507.04632].
• A. Marchesiello, S. Post, L. Snobl, Third-order superintegrable systems with potentials satisfying only nonlinear equations, J. Math. Phys. 56 (2015) 102104 [arXiv:1501.00470].
• Libor Snobl and Pavel Winternitz: Classification and Identification of Lie Algebras, CRM Monograph Series, Volume: 33, American Mathematical Society together with Centre de Recherches Mathematiques, ISBN-13: 978-0-8218-4355-0 (a short presentation).
• L. Hlavaty, J. Navratil and L. Snobl, On renormalization of Poisson-Lie T-plural sigma models , Acta Polytechnica (2013) to appear [arXiv:1212.5936].
• L. Snobl and P. Winternitz, Solvable Lie algebras with Borel nilradicals, J. Phys. A: Math. Theor. 45 (2012) 095202 [arXiv:1110.5492].
• L. Snobl, Maximal solvable extensions of filiform algebras, Archivum mathematicum 47 (2011) 405-414.
• A.M. Grundland, A.J. Hariton and L. Snobl, Invariant solutions of supersymmetric nonlinear wave equations, J. Phys. A: Math. Theor. 44 (2011) 085204 [arXiv:0911.1324].
• L. Snobl, On the structure of maximal solvable extensions and of Levi extensions of nilpotent Lie algebras, J. Phys. A: Math. Theor. 43 (2010) 505202 [arXiv:1003.4223].
• L. Snobl and D. Karasek, Classification of solvable Lie algebras with a given nilradical by means of solvable extensions of its subalgebras, Linear Algebra and its Applications 432 (2010) 1836-1850, [arXiv:0908.0271].
• A. M. Grundland, A. J. Hariton and L. Snobl, Invariant solutions of the supersymmetric sine-Gordon equation, J. Phys. A: Math. Theor. 42 (2009) 335203. [arXiv:0812.3862].
• L. Snobl and P. Winternitz, All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1, J. Phys. A: Math. Theor. 42 (2009) 105201 [arXiv:0809.3259].
• L. Hlavaty and L. Snobl, Description of D-branes invariant under the Poisson-Lie T-plurality, J. High Energy Phys. 07 (2008) 122 [arXiv:0806.0963].
• C. Albertsson, L. Hlavaty, and L. Snobl, On the Poisson-Lie T-plurality of boundary conditions, J. Math. Phys. 49 (2008) 032301, [arXiv:0706.0820]. Presentation in Stockholm.
• L. Hlavaty and L. Snobl, Poisson-Lie T-plurality as canonical transformation, Nucl. Phys. B 768 (2007) 209-218, [hep-th/0608133].
• A.M. Grundland and L. Snobl, Surfaces Associated with Sigma Models, Studies in Applied Mathematics 117 (2006) 335-351 (the preliminary version available as [math.DG/0601302] differs substantially from the published paper).
• L. Hlavaty and L. Snobl, Transformations of conformally invariant sigma models, Proceedings of the 25th Winter School Geometry and Physics, Srni, January 2005, Rend. Cic. Mat. Palermo, Serie II, Suppl. 79 (2006) 111-116.
• A. M. Grundland and L. Snobl, Description of surfaces associated with Grassmannian sigma models on Minkowski space, J. Math. Phys. 46 (2005) 083508 [math.DG/0501200].
• L. Snobl and P. Winternitz, A class of solvable Lie algebras and their Casimir Invariants, J. Phys. A: Math. Gen. 38 (2005) 2687-2700, [math-ph/0411023].
• L. Hlavaty and L. Snobl, Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle, J. High Energy Phys. 10 (2004) 045, [hep-th/0408126].
• A.M. Grundland and L. Snobl, Surfaces in su(N) algebra via CP^{N-1} sigma models on Minkowski space, Proceedings of International Conference Symmetry Methods in Physics [CD-ROM]. Dubna: JINR, 2004.
• A. M. Grundland and L. Snobl, Description of surfaces associated with CP^(N-1) sigma models on Minkowski space, Journal of Geometry and Physics 56 (2006) 512-531, [math.DG/0405513].
• L. Hlavaty and L. Snobl, Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models, J. High Energy Phys. 05 (2004) 010 [hep-th/0403164].
• L. Snobl, Modular spaces of low-dimensional Drinfeld doubles, Proceedings of the 23rd Winter School Geometry and Physics, Srni, January 2003, Rend. Cic. Mat. Palermo, Serie II, Suppl. 72 (2004) 193-202.
• L. Snobl, On modular spaces of semisimple Drinfeld doubles, J. High Energy Phys. 09 (2002) 018 [hep-th/0204244].
• Doctoral Thesis.
• L. Snobl, L. Hlavaty, Classification of 6-dimensional real Drinfeld doubles, Int. J. Mod. Phys. A17 (2002) 4043-4068 [math.QA/0202210].
• L. Hlavaty, L.Snobl, Classification of 6-dimensional Manin triples, [math.QA/0202209]
• L. Hlavaty, L. Snobl, Classification of Poisson-Lie T-dual models with two-dimensional targets, Mod. Phys. Lett. A17 (2002) 429-434 [hep-th/0110139].
• L. Snobl, L. Hlavaty, Principal chiral models with non-constant metric, Czech. J. of Phys. 51 (2001) 1441-1446.
• L Hlavaty and L Snobl, Principal chiral models on non-semisimple groups, J. Phys A 34 (2001) 7795-7809.
• L. Snobl, Construction of quantum doubles from solutions of Yang-Baxter system, Czech. J. of Phys. 50 (2000) 187-192.
• L. Hlavaty, L. Snobl, Solution of the Yang-Baxter System for Quantum Doubles, Int. J. Mod. Phys. A 14 (1999) 3029-3058.
• L. Hlavaty, L. Snobl, Solution of a Yang-Baxter system, [math.QA/9811016] (a preliminary version of the article above).
• Diploma Thesis: Quantum doubles and Universal R-matrices, Prague 1999.
• Pre-Diploma work: Solution of the Yang-Baxter System for Quantum doubles, Prague 1998 (in czech, for english version see articles above).
• Review work: Bethe's Ansatz and Yang-Baxter Equations, Prague 1997 (in czech only).

List of conferences and talks:
• Analytic and algebraic methods in physics XIX , Prague, September 2022, (talk Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion).
• 34th International Colloquium on Group Theoretical Methods in Physics , Strasbourg, July 2022, (talk Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion).
• Group theoretical methods in physics, A commemorative meeting in honour of Pavel Winternitz at the CRM , Montreal, July 2021, (talk Superintegrability in the presence of magnetic fields: the cylindrical case).
• Analytic and algebraic methods in physics XVI , Prague, September 2019, (talk Superintegrability and time - dependent integrals).
• XI. International Symposium Quantum Theory and Symmetries, Montreal, July 2019 (talk Superintegrability in the presence of magnetic fields).
• 32th International Colloquium on Group Theoretical Methods in Physics, Prague, July 2018, (talk Integrable 3D systems in a magnetic field corresponding to spherical separation of variables).
• Symmetry and Perturbation Theory, Pula, Sardinia, June 2018, (talk Spherical type integrable classical systems in a magnetic field).
• Group Analysis of Differential Equations and Integrable Systems, Larnaca, June 2018, (talk Integrable 3D systems in a magnetic field corresponding to spherical separation of variables).
• Physics and Mathematics of Nonlinear Phenomena, Gallipoli, June 2017, (talk Superintegrable 3D systems in a magnetic field corresponding to Cartesian separation of variables).
• Doppler Institute-CRM Workshop on the occasion of 80th birthdays of Jiri Patera and Pavel Winternitz, Prague, June 2016, (talk Integrable and superintegrable systems in static electromagnetic fields).
• Physics and Mathematics of Nonlinear Phenomena, Gallipoli, June 2015, (talk 3D superintegrable systems with magnetic field).
• Exact Solvability and Symmetry Avatars, CRM Montreal, August 2014, (talk Classification and Identification of Lie Algebras).
• 30th International Colloquium on Group Theoretical Methods in Physics, Ghent, July 2014, (talk Classification and Identification of Lie Algebras).
• Group Analysis of Differential Equations and Integrable Systems, Larnaca, June 2014, (talk Classification and identification of Lie algebras). Analytic and algebraic methods in physics XII, the meeting dedicated to the 75th birthday of professor Miloslav Havlicek, Prague, November 2013 (talk Classification and Identification of Lie Algebras).
• 7th Student Colloquium and School on Mathematical Physics, Stara Lesna, August 2013 (lecture series Superintegrability in classical and quantum mechanics).
• Symmetries in Science XVI, Bregenz, July 2013, (talk Classification of solvable & Levi decomposable Lie algebras).
• The 33th Winter School GEOMETRY AND PHYSICS, Srni, January 2013 (talk Solvable Lie algebras with Borel nilradicals).
• Student Colloquium and School on Mathematical Physics, Stara Lesna, August 2012 (lecture Solvable Lie algebras with Borel nilradicals).
• Group Analysis of Differential Equations and Integrable Systems, Protaras, Cyprus, June 2012 (lecture Solvable Lie algebras with Borel nilradicals).
• 50. Internationale Universitaetswochen fuer Theoretische Physik "Prospects of Particle Physics", Schladming, February 2012.
• The 28th Nordic Network Meeting on "Strings, Fields and Branes", Stockholm, December 2011.
• Student Colloquium and School on Mathematical Physics, Stara Lesna, August 2011 (minicourse Representations of Lie algebras, Casimir operators and their applications).
• VII. International Symposium QUANTUM THEORY AND SYMMETRIES, Prague, August 2011 (talk Structure of Levi extensions of nilpotent and solvable Lie algebras).
• 49. Internationale Universitaetswochen fuer Theoretische Physik "Physics at all scales: The Renormalization Group", Schladming, February/March 2011.
• The 31th Winter School GEOMETRY AND PHYSICS, Srni, January 2011 (talk Structure of Levi extensions of nilpotent and solvable Lie algebras).
• Workshop Symmetries and Lagrangian Formalism in Geometry & Physics: A homage to Jerrold E. Marsden, Madrid, November 2010 (talk Poisson-Lie T-plurality and invariant D-branes).
• Symmetry, Separation, Super-integrability and Special Functions (S4) Conference, Minneapolis, September 2010 (talk Classification of solvable Lie algebras - new approaches and developments).
• International Conference on Strings, M-theory and Quantum Gravity, Ascona, July 2010.
• Orbit functions, Workshop of the Doppler Institute, Decin, June 2010.
• Group Analysis of Differential Equations and Integrable Systems, Fifth Workshop, Protaras, Cyprus, June 2010 (talk Symmetries and invariant solutions of PDEs on superspace).
• 48. Internationale Universitaetswochen fuer Theoretische Physik "Masses and Constants", Schladming, March 2010 (seminar Symmetries and invariant solutions of PDEs on superspace).
• The 30th Winter School GEOMETRY AND PHYSICS, Srni, January 2010 (talk Classification of solvable Lie algebras with a given nilradical by means of solvable extensions of its subalgebras).
• Student Colloquium and School on Mathematical Physics, Stara Lesna, August 2009 (minicourse Classification of Lie algebras).
• XVI International Congress on Mathematical Physics and Young Researcher Symposium, Prague, August 2009 (talk Description of D-branes invariant under the Poisson-Lie T-plurality transformations).
• Symposium Symmetries in Science, Bregenz, July 2009.
• The 29th Winter School GEOMETRY AND PHYSICS, Srni, January 2009 (talk Symmetries and invariant solutions of the supersymmetric sine-Gordon equation).
• Geometrical Aspects of String Theory, Stockholm, October 2008.
• Strings 2008, CERN, Geneva, August 2008.
• Poisson 2008, Lausanne, July 2008 (poster Description of D-branes invariant under the Poisson-Lie T–plurality transformations).
• The 28th Winter School GEOMETRY AND PHYSICS, Srni, January 2008 (talk Poisson-Lie T-plurality of boundary conditions).
• Autumn Student School on Mathematical Physics, Stara Lesna, July 2007 (talk On Poisson-Lie T-plurality of boundary conditions).
• Eurostrings07, Orthodox Academy of Crete, Kolymbari, Crete, July 2007.
• Summer School Aspects of Membrane Dynamics, Stockholm, June 2007 (talk On Poisson-Lie T-plurality of boundary conditions).
• Winter School "Geometry and Physics", Srni, January 2007 (talk Poisson-Lie T-plurality as canonical transformation).
• School on Particle Physics, Gravity and Cosmology, Dubrovnik, August-September 2006. Proceedings.
• Geometry and the Universe, C.N. Yang Institute, Stony Brook, October 2005.
• IV. International Symposium QUANTUM THEORY AND SYMMETRIES, Varna, August 2005 (talk On the classification of solvable Lie algebras with given nilradicals).
• Strings05, Toronto, July 2005 (a poster Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models).
• Summer School on Strings, Gravity and Cosmology, Perimeter Institute, Waterloo, June-July 2005 (student talk Poisson-Lie T-plurality and 3-dimensional conformally invariant sigma models), scanned lecture notes (taken during the lectures, i.e. fairly uncomplete).
• Winter School "Geometry and Physics", Srni, January 2005 (talk Description of surfaces associated with Grassmannian sigma models on Minkowski space).
• XI International Conference on Symmetry Methods in Physics, Prague, June 2004 (talk The structural equations of surfaces associated with CP^{N-1} sigma models on Minkowski space.).
• XIII International Colloquium on Integrable Systems and Quantum Groups, Prague, June 2004 (talk Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models.).
• 61ieme Colloque des sciences mathematiques du Quebec, Montreal, April 24, 2004 (talk Poisson-Lie T-plurality and 3-dimensional conformally invariant sigma models.).
• Winter School "Geometry and Physics", Srni, January 2004.
• XIV International Congress on Mathematical Physics, University of Lisbon, July - August 2003 (a poster On modular spaces of Drinfeld doubles).
• School on Mathematics in String and Field Theory , ICTP Trieste, June 2003
  scanned lecture notes (taken during the lectures, i.e. fairly uncomplete).
• Winter School "Geometry and Physics", Srni, January 2003 (talk "Modular spaces of Drinfeld doubles").
• International Conference on Theoretical Physics , Paris, UNESCO, July 2002 (a poster Classification of Poisson-Lie T-dual models with two-dimensional targets).
• XXIV International Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (a poster Classification of six-dimensional real Manin triples and Drinfeld doubles).
• Introductory School on String Theory , ICTP Trieste, June 2002 scanned lecture notes (taken during the lectures, i.e. fairly uncomplete).
• Winter School "Geometry and Physics", Srni, January 2002 (talk Poisson-Lie T-dual models with two dimensional targets).
• Euro Summer School "WHAT IS INTEGRABILITY?", Cambridge, August 2001 scanned lecture notes (taken during the lectures, i.e. fairly uncomplete).
• XX Workshop on Geometric Methods in Physics, Bialowieza, July 2001 (talk Principal chiral models with non-constant metric).
• 10th Colloquium "Quantum Groups and Integrable Systems", Prague, June 2001 (talk Principal chiral models with non-constant metric).
• Winter School "Geometry and Physics", Srni, January 2001 (talk Principal chiral models on non-semisimple groups).
• Workshop on Algebraic Geometry and Physics "Algebraic Geometry and Integrable Systems", SISSA, Trieste, October 2000.
• XIII International Congress on Mathematical Physics, Imperial College, London, July 2000 (talk Solution of the Yang-Baxter System for Quantum Doubles and a poster Construction of Quantum Doubles from Solutions of Yang-Baxter System).
• 39. Internationale Universitaetswochen fuer Kern- und Teilchenphysik "Methods of Quantization", Schladming, February-March 2000 (talk Construction of quantum doubles from solutions of Yang-Baxter system).
• XVIII Workshop on Geometric Methods in Physics, Bialowieza, July 1999 (talk Construction of quantum doubles from solutions of Yang-Baxter system).
• Winter School "Geometry and Physics", Srni, January 1999.
• 8th Colloquium "Quantum Groups and Integrable Systems", Prague, June 1999 (talk Construction of quantum doubles from solutions of Yang-Baxter system).
• South European School on Elementary Particle Physics, Corfu, September 1998.