Quadratic Poisson brackets and Drinfel'd theory for associative algebras
q-alg
2016-09-08 v1 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.q-alg/9501019,
title = {Quadratic Poisson brackets and Drinfel'd theory for associative algebras},
author = {A. A. Balinsky and Yu. M. Burman},
journal= {arXiv preprint arXiv:q-alg/9501019},
year = {2016}
}
Comments
latex, no figures.