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 talk I will present a general setting for a compactly generated tensor triangulated category which enables one to classify thick tensor ideals and the spectrum Spc. Several examples involving Lie algebra/Lie superalgebras and quantum groups will be presented where we show how to construct a Zariski spaces and demonstrate how these topological spaces governs the tensor triangulated geometry for various categories. If time permits, I will also explain recent results that generalize these ideas to the non-commutative setting.