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Tensor Triangular Geometry with Applications to Classical Lie Superalgebras

Banff International Research Station for Mathematical Innovation and Discovery

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. Examples will be given which illustrate the interactions between the algebra and the geometry. For a classical Lie superalgebra g, I will show how to construct a Zariski space from a detecting subalgebra f and demonstrate that this topological space governs the tensor triangular geometry for the category of finite dimensional g-modules which are semisimple over g_0. A complete determination of thick tensor ideals and Spc will be given for the Lie superalgebra gl(m|n). Conjectures will be presented for arbitrary classical Lie superalgebras. These results represent joint work with Brian Boe and Jonathan Kujawa.

Mathematics; Category theory; homological algebra; Algebraic structures

video/mp4

Author affiliation: University of Georgia

2017-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60065

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/