Lie antialgebras: cohomology and representations

TL;DR

This paper explores the algebraic and geometric properties of Lie antialgebras, focusing on their cohomology, representations, origins, classification, and examples, contributing to the understanding of their structure and applications.

Contribution

It introduces classification theorems and discusses the cohomology and representations of Lie antialgebras, expanding the theoretical framework of this algebraic class.

Findings

Description of algebraic and geometric properties

Formulation of classification theorems

Examples illustrating the concepts

Abstract

We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We formulate classification theorems and give a number of examples.