Typical blocks of Lie superalgebras in prime characteristic

TL;DR

This paper establishes an equivalence between typical blocks of modules over Lie superalgebras and their even parts in prime characteristic, providing new insights into their representation theory.

Contribution

It introduces an equivalence of categories for typical blocks of Lie superalgebra modules and their even subalgebras in prime characteristic.

Findings

Equivalence of categories for typical blocks established

Consequences for representation theory derived

Simplifies understanding of Lie superalgebra modules

Abstract

For a type I basic classical Lie superalgebra $\mathfrak{g}=\mathfrak{g}_{\bar{0}} \oplus \mathfrak{g}_{\bar{1}}$, we establish an equivalence between typical blocks of categories of $U_{\chi}(\mathfrak{g})$-modules and $U_{\chi}(mathfrak{g}_{\bar{0})$-modules. We then deduce various consequences from the equivalence.