Tensor Triangular Geometry for Classical Lie Superalgebras

Abstract

Tensor triangular geometry as introduced by Balmer is a powerful idea which can be used to extract the ambient geometry from a given tensor triangulated category. In this paper we provide a general setting for a compactly generated tensor triangulated category which enables one to classify thick tensor ideals and the Balmer spectrum. For a classical Lie superalgebra $\mathfrak{g}={\mathfrak{g}}_{\bar{0}}\oplus {\mathfrak{g}}_{\bar{1}}$, we construct a Zariski space from a detecting subalgebra of $\mathfrak{g}$ and demonstrate that this topological space governs the tensor triangular geometry for the category of finite dimensional $\mathfrak{g}$-modules which are semisimple over ${\mathfrak{g}}_{\bar{0}}$.

to appear in Advances in Mathematics