Typical blocks of Lie superalgebras in prime characteristic

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.