Publication date:
9 July 2017
Source:Advances in Mathematics, Volume 314
Author(s): Brian D. Boe, Jonathan R. Kujawa, Daniel K. Nakano
Tensor triangular geometry as introduced by Balmer [3] 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 the general linear Lie superalgebra $\mathfrak{g}={\mathfrak{g}}_{\overline{0}}\oplus {\mathfrak{g}}_{\overline{1}}$ 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 ${\mathfrak{g}}_{\overline{0}}$.