论文标题
$ 2 $维代数的保守代数，iv
Conservative algebras of $2$-dimensional algebras, IV
论文作者
论文摘要
保守派代数的概念出现在坎托（Kantor）于1972年的一篇论文中。后来，他在$ n $ dimensional vector Space上定义了所有代数（即双线图）的保守代数$ w（n）$。如果$ n> 1 $，则代数$ w（n）$不属于任何众所周知的代数类（例如联想，Lie，Jordan或Leibniz代数）。保守代数理论中的$ w（n）$看起来与$ \ mathfrak {gl} _n $在Lie代数理论中的作用相似。也就是说，可以从\ mathbb {n}的某些$ n \ in \ mathbb {n}中的普遍代数$ w（n）$中获得任意保守的代数。
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra $W(n)$ does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). It looks like $W(n)$ in the theory of conservative algebras plays a similar role to the role of $\mathfrak{gl}_n$ in the theory of Lie algebras. Namely, an arbitrary conservative algebra can be obtained from a universal algebra $W(n)$ for some $n \in \mathbb{N}.$ The present paper is a part of a series of papers, dedicated to the study of the algebra $W(2)$ and its principal subalgebras.
