publication . Article . Preprint . 1994

quadratic poisson brackets compatible with an algebra structure

Balinsky, A. A.; Burman, Yu.;
Open Access
  • Published: 21 Sep 1994 Journal: Journal of Physics A: Mathematical and General, volume 27, pages L693-L696 (issn: 0305-4470, eissn: 1361-6447, Copyright policy)
  • Publisher: IOP Publishing
Abstract
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
Subjects
arXiv: Mathematics::Quantum AlgebraNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics::Symplectic Geometry
free text keywords: Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics, Algebraic structure, Bracket, First class constraint, Mathematics, Bracket (mathematics), Poisson bracket, Mathematical analysis, Poisson algebra, Algebra, Vector space, Operator algebra, High Energy Physics - Theory, Mathematics - Quantum Algebra

[1] Drinfeld V G 1986 Quantum groups Proc. of the International Congress of Math., vol 1 (Berkeley, CA: Academic) pp 798-820

[2] Sklyanin E K 1982 Funct. Anal. Appl., 16 263 and 17 273

[3] Kupershmidt B A 1993 A q-analogue of the dual space to the Lie algebras gl(2) and sl(2) J. Phys. A:Math. Gen. 26, L1-L4 [OpenAIRE]

[4] Kupershmidt B A 1993 All quantum group structures on the supergroup GL(1|1) J. Phys. A:Math. Gen. 26, L251-L256

[5] Kupershmidt B A 1994 Poisson relation between minors and their consequences preprint [OpenAIRE]

[6] Faddeev L D, Reshetikhin N Yu and Takhtajan L A 1989 Quantization of Lie groups and Lie algebras Alg. Anal, 1 , 178

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 1994

quadratic poisson brackets compatible with an algebra structure

Balinsky, A. A.; Burman, Yu.;