Support for integrable Hopf algebras via noncommutative hypersurfaces

2020/05/06 by Negron, Cris, Pevtsova, Julia · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2005.02965

Abstract

We consider finite-dimensional Hopf algebras u which admit a smooth deformation U→ u by a Noetherian Hopf algebra U of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers, restricted enveloping algebras in finite characteristic, and Drinfeld doubles of height 1 group schemes. We provide a means of analyzing (cohomological) support for representations over such u, via the singularity categories of the hypersurfaces U/(f) associated to functions f on the corresponding parametrization space. We use this hypersurface approach to establish the tensor product property for cohomological support, for the following examples: functions on a finite group scheme, Drinfeld doubles of certain height 1 solvable finite group schemes, bosonized quantum complete intersections, and the small quantum Borel in type A.

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