Noncommutative Tensor Triangular Geometry and the Tensor Product Property for Support Maps
| Autor: | Milen Yakimov, Kent B. Vashaw, Daniel K. Nakano |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Triangulated category General Mathematics Characterization (mathematics) 01 natural sciences Spectrum (topology) Tensor (intrinsic definition) Mathematics - Quantum Algebra 0103 physical sciences Lie algebra FOS: Mathematics Quantum Algebra (math.QA) Category Theory (math.CT) Representation Theory (math.RT) 0101 mathematics Mathematics 010102 general mathematics Mathematics - Category Theory Mathematics - Rings and Algebras Hopf algebra Noncommutative geometry Tensor product Rings and Algebras (math.RA) 010307 mathematical physics Mathematics - Representation Theory 18G80 18M05 17B37 |
| Zdroj: | International Mathematics Research Notices. 2022:17766-17796 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnab221 |
| Popis: | The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier developments on representations of finite group schemes. Many authors have focussed on concrete situations where positive and negative results have been obtained by direct arguments. In this paper we demonstrate that it is natural to study questions involving the tensor product property in the broader setting of a monoidal triangulated category. We give an intrinsic characterization by proving that the tensor product property for the universal support datum is equivalent to complete primeness of the categorical spectrum. From these results one obtains information for other support data, including the cohomological one. Two theorems are proved giving compete primeness and non-complete primeness in certain general settings. As an illustration of the methods, we give a proof of a recent conjecture of Negron and Pevtsova on the tensor product property for the cohomological support maps for the small quantum Borel algebras for all complex simple Lie algebras. 20 pages |
| Databáze: | OpenAIRE |
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