Abstract

Let $R\subseteq E$ be two Lie conformal algebras and Q be a given complement of R in E. Classifying complements problem asks for describing and classifying all complements of R in E up to an isomorphism. It is known that E is isomorphic to a bicrossed product of R and Q. We show that any complement of R in E is isomorphic to a deformation of Q associated to the bicrossed product. A classifying object is constructed to parameterize all R-complements of E. Several explicit examples are provided. Similarly, we also develop a classifying complements theory of associative conformal algebras.

中文翻译：

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保形代数的分类补码

摘要

让 $\mathrm{电阻}\subseteq 乙$是两个李代数形和Q是给定的补充[R在ë。分类补这道题用于描述和分类的所有补[R在ë长达一个同构。已知E与R和Q的双交叉产物同构。我们表明，任何补[R在ë是同构的变形Q关联到bicrossed产品。构造一个分类对象来参数化E 的所有R -补码. 提供了几个明确的例子。同样，我们还开发了结合共形代数的分类补码理论。