Quadratic Poisson brackets and Drinfel'd theory for associative algebras

Abstract

Quadratic Poisson brackets on associative algebras are studied. Such a bracket compatible with the multiplication is related to a differentiation in tensor square of the underlying algebra. Jacobi identity means that this differentiation satisfies a classical Yang--Baxter equation. Corresponding Lie groups are canonically equipped with a Poisson Lie structure. A way to quantize such structures is suggested.

arXiv commentlatex, no figures.

References in corpus (2)

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