Tensor Triangular Geometry for Classical Lie Superalgebras
| Autor: | Boe, Brian D., Kujawa, Jonathan R., Nakano, Daniel K. |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 ${\mathfrak g}_{\bar{0}}$. Comment: to appear in Advances in Mathematics |
| Databáze: | arXiv |
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