Twisting Poisson algebras, coPoisson algebras and Quantization
Abstract
The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson algebras or bialgebras and star-products. We con- sider Hom-algebraic structures generalizing classical algebraic structures by twisting the identities by a linear self map. We summarize the results on Hom-Poisson algebras and introduce Hom-coPoisson algebras and bialge- bras. We show that there exists a duality between Hom-Poisson bialgebras and Hom-coPoisson bialgebras. A relationship between enveloping Hom- algebras endowed with Hom-coPoisson structures and corresponding Hom- Lie bialgebra structures is studied. Moreover we set quantization problems and generalize the notion of star-product. In particular, we characterize the twists for the Moyal-Weyl product for polynomials of several variables.
Cite
@article{arxiv.1205.0683,
title = {Twisting Poisson algebras, coPoisson algebras and Quantization},
author = {Martin Bordemann and Olivier Elchinger and Abdenacer Makhlouf},
journal= {arXiv preprint arXiv:1205.0683},
year = {2012}
}