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RESEARCH PRODUCT
Module categories of finite Hopf algebroids, and self-duality
Peter Schauenburgsubject
Self-duality[ MATH ] Mathematics [math]Finite tensor categoryGeneral MathematicsDuality (mathematics)Representation theory of Hopf algebrasBimodulesQuasitriangular Hopf algebra01 natural sciencesMonoidal CategoriesMathematics::Category TheoryMathematics::Quantum Algebra0103 physical sciencesRings0101 mathematicsAlgebra over a fieldAbelian group[MATH]Mathematics [math]Fusion categoryHopf algebroidMSC: Primary 16T99 18D10SubfactorsMathematicsQuantum groupApplied Mathematics010102 general mathematicsMathematics::Rings and AlgebrasTensor CategoriesTheorem16. Peace & justiceHopf algebraDual (category theory)Algebra010307 mathematical physicsWeak Hopf algebradescription
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-01 |