Tensor Triangular Geometry for Classical Lie Superalgebras

2014/02/15 by Boe, Brian D., Kujawa, Jonathan R., Nakano, Daniel K.
#17B10 #17B56 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1402.3732

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_0⊕ \mathfrak g_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_0.

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