On Algebras Associated with Integrable Hamiltonian Systems
University of Zielona Góra, Institute of Physics,
ul. Szafrana 4a, 65-516 Zielona Góra, Poland
e-mail: S.Kasperczuk@if.uz.zgora.pl
Received:
Received: 23 March 2010; accepted: 8 July 2010; published online: 13 September 2010
DOI: 10.12921/cmst.2010.16.02.161-163
OAI: oai:lib.psnc.pl:724
Abstract:
The aim of this paper is to give a general setting, based on quantum deformations, for the explicit construction of certain classes of integrable Hamiltonian systems.
Key words:
Casimir functions, Hamiltonian systems, integrability, Poisson bialgebras, quantum deformations
References:
[1] S. Kasperczuk, Cel. Mech. Dyn. Astron. 76, 215 (2000).
[2] S. Kasperczuk, Physics A 284, 113 (2000).
[3] S. Kasperczuk, Acta Physica Polonica B 34, 11 (2003).
[4] M.A.E. Sweedler, Hopf Algebras, Reading. MA: Adison- Wesley, New York 1969.
[5] S. Maijd, Foundations of Quantum Groups Theory. Camberidge Univ. Press 1995.
[6] Chari, A. Pressley, A Guide to Quantum Groups. Camberidge Univ. Press 2000.
[7] A. Weinstein, J. Diff. Geom. 18, 523 (1983).
The aim of this paper is to give a general setting, based on quantum deformations, for the explicit construction of certain classes of integrable Hamiltonian systems.
Key words:
Casimir functions, Hamiltonian systems, integrability, Poisson bialgebras, quantum deformations
References:
[1] S. Kasperczuk, Cel. Mech. Dyn. Astron. 76, 215 (2000).
[2] S. Kasperczuk, Physics A 284, 113 (2000).
[3] S. Kasperczuk, Acta Physica Polonica B 34, 11 (2003).
[4] M.A.E. Sweedler, Hopf Algebras, Reading. MA: Adison- Wesley, New York 1969.
[5] S. Maijd, Foundations of Quantum Groups Theory. Camberidge Univ. Press 1995.
[6] Chari, A. Pressley, A Guide to Quantum Groups. Camberidge Univ. Press 2000.
[7] A. Weinstein, J. Diff. Geom. 18, 523 (1983).
