Lie antialgebras: premices

Valentin Ovsienko

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arXiv · 0705.1629

Lie antialgebras: premices

Valentin Ovsienko

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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 $\mathbbZ_2$-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.

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BibTeX RIS

Valentin Ovsienko. 2010-10-15. Lie antialgebras: premices. https://arxiv.org/abs/0705.1629

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