Module categories of finite Hopf algebroids, and self-duality | Zendy

Peter Schauenburg | Zendy

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Module categories of finite Hopf algebroids, and self-duality

Author(s) -

Peter Schauenburg

Publication year - 2015

Publication title -

transactions of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.798

H-Index - 100

eISSN - 1088-6850

pISSN - 0002-9947

DOI - 10.1090/tran6687

Subject(s) - hopf algebra , mathematics , quasitriangular hopf algebra , dual (grammatical number) , duality (order theory) , pure mathematics , abelian group , representation theory of hopf algebras , algebra over a field , linguistics , cellular algebra , philosophy , algebra representation

International audienceWe 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

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