Quadratic Poisson brackets and Drinfeld theory for associative algebras

Abstract

The paper is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang--Baxter equation are revealed. The paper also contains a description of Poisson Lie structures on Lie groups whose Lie algebras are adjacent to an associative structure.

arXiv comment16 pages, latex, no figures

References in corpus (2)

• Quadratic Poisson brackets compatible with an algebra structure
• Generalized quantization scheme for central extensions of Lie algebras