Induced modules for modular Lie algebras

Abstract

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional $S$-modules. Then there exists a category $C$ of finite-dimensional $L$-modules containing the modules in $X$ such that the restriction functor Res$:C\to D$ has a left adjoint Ind$:D\to C$.

8 pages. Version 5 acknowledges priority and adds reference to relevant paper of Farnsteiner

References in corpus (1)

• Character clusters for Lie algebra modules over a field of non-zero characteristic

Cited by in corpus (2)

• Blocks of representations of Lie algebras
• On $\mathfrak{F}$-hypercentral modules and character clusters