Lie antialgebras: premices
Mathematical Physics
2010-10-18 v6 math.MP
Quantum Algebra
Symplectic Geometry
Abstract
The main purpose of this work is to develop the basic notions of the Lie theory for commutative algebras. We introduce a class of -graded commutative but not associative algebras that we call ``Lie antialgebras''. These algebras are closely related to Lie (super)algebras and, in some sense, link together commutative and Lie algebras. The main notions we define in this paper are: representations of Lie antialgebras, an analog of the Lie-Poisson bivector (which is not Poisson) and central extensions. We also classify simple finite-dimensional Lie antialgebras.
Keywords
Cite
@article{arxiv.0705.1629,
title = {Lie antialgebras: premices},
author = {Valentin Ovsienko},
journal= {arXiv preprint arXiv:0705.1629},
year = {2010}
}