Quadratic Poisson brackets compatible with an algebra structure

Preprint English OPEN
Balinsky, A. A.; Burman, Yu.;
(1994)
  • Related identifiers: doi: 10.1088/0305-4470/27/18/008
  • Subject: High Energy Physics - Theory | Mathematics - Quantum Algebra
    arxiv: Mathematics::Quantum Algebra | Mathematics::Symplectic Geometry | Nonlinear Sciences::Exactly Solvable and Integrable Systems

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 c... View more
  • References (6)

    [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

    [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

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

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