论文标题
分类保形代数的补充
Classifying complements for conformal algebras
论文作者
论文摘要
令$ r \ subseteq e $为两个谎言保形代数，$ q $是$ e $中的$ r $的补充。分类的补充问题要求描述和分类$ e $ e $ in $ e $的所有补充，以构成同构。众所周知，$ e $是$ r $和$ q $的两种产品的同构。我们表明，$ e $中的$ r $ $ $ $的任何补充都是与$ q $相关的$ q $的同构。构建了一个分类对象，以参数化$ e $的所有$ r $ - 汇总。提供了几个明确的例子。同样，我们还开发了一个分类的辅助保形代数理论。
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.
