Quadratic Poisson Brackets and the Drinfeld Theory for Associative Algebras

Letters in Mathematical Physics

Volumn 38, Issue 1, 1996, Pages 63-75

  Balinsky, A ^a   Burman, Yu ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Associative algebra; Poisson brackets; Yang baxter equation

Indexed keywords

EID: 0003034469     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00398299     Document Type: Article

References (11)

1. Drinfeld, V. G.: Hamiltonian structures on Lie groups, Lie bialgebras and geometric meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 268 (1983), 285-287.
2. Balinsky, A. A.: Generalized quantization scheme for central extensions of Lie algebras, J. Phys. A: Math. Gen. 27, (1994), L87-L90.
3. Kupershmidt, B. A.: A q-analogue of the dual space of the Lie algebras gl(2) and sl(2), J. Phys. A: Math. Gen. 26 (1993), L1-L4.
4. Kupershmidt, B. A.: All quantum group structures on the supergroup GL(1|1), J. Phys. A: Math. Gen. 26 (1993), L251-L256.
5. Kupershmidt, B. A.: Poisson relations between minors and their consequences, Preprint, 1994.
6. Semenov-Tyan-Shansky, M. A.: What is classical R-matrix? Funct. Anal. Appl. 17 (17) (1983), 259-272.
7. Manin, Yu.: Quantum groups and non-commutative geometry, Montreal preprint, 1988.
8. Drinfeld, V. G.: Quantum groups, in Proc. ICM86, volume 1, Berkeley 1 (1987), 798-820.
9. Sklyanin, E. K.: Some algebraic structure connected with the Yang-Baxter equation, Funct. Anal. Appl. 17 (1982), 263-270.
10. Balinsky, A. A. and Burman, Yu. M.: Quadratic poisson brackets compatible with an algebra structure, J. Phys. A: Math. Gen. 27 (1994), L693-L696.
11. Kupershmidt, B. A.: Conformally multiplicative poisson structures in linear algebra and algebraic geometry, in: J. Harnad and J. E. Marsden (eds), Hamiltonian Systems, Transformation Groups and Spectral Transform Methods, 1990, pp. 177-188.