李反代数：前提
Lie antialgebras: premices
摘要：
这项工作的主要目的是发展交换代数的李理论的基本概念。引入了一类$\mathbbZ_2$ -分次交换但非结合的代数，我们称之为“李反代数”。这些代数与李（超）代数密切相关，并且在某种意义上将交换代数和李代数联系在一起。我们在本文中定义的主要概念是：表示李反代数，一个类似的李泊松双向量（这不是泊松）和中心扩展。我们还对简单的有限维李反代数进行了分类。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
