Support data for Hopf algebras via noncommutative hypersurfaces - with Julia Pevtsova

Abstract: In recent work with J. Pevtsova, we develop an approach to support theory for Hopf algebras via noncommutative hypersurfaces. As a starting point, one considers a Hopf algebra u which admits a smooth deformation U → u by a Noetherian Hopf algebra U of finite global dimension. One uses this deformation to produce a rank variety for u which takes values in an associated projective space. Our work is inspired by earlier contributions of Avramov and Buchweitz, which concerned support for (commutative) local complete intersections. I will discuss some modular examples, functions on finite group schemes and Drinfeld doubles of infinitesimal group schemes, and also quantum groups over the complexes. I will discuss how one can use this hypersurface approach to address the tensor product property in certain “solvable” examples.

commutative algebraalgebraic topologyquantum algebrarepresentation theory

Audience: researchers in the topic

DG methods in commutative algebra and representation theory

Series comments: Description: Online special session

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