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Title: Noncommutative Tensor Triangular Geometry and the Tensor Product Property for Support Maps
Abstract 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 focused 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.  more » « less
Award ID(s):
2131243
PAR ID:
10332729
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
International Mathematics Research Notices
ISSN:
1073-7928
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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