On module categories over finite-dimensional Hopf algebras
By N. Andruskiewitsch, Juan Martín Mombelli. 2006
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Abstract We show that indecomposable exact module categories over the category RepH of representations of a finite-dimensional Hopf algebra H are classified by left comodule algebras, H-simple from the right and with trivial coinvariants, up to equivariant Morita equivalence. Specifically, any indecomposable exact module category is equivalent to the category of finite-dimensional modules over a left comodule algebra. This is an alternative approach to the results of Etingof and Ostrik. For this, we study the stabilizer introduced by Yan and Zhu and show that it coincides with the internal Hom. We also describe the correspondence of module categories between RepH and Rep ( H ∗ ) .
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4a9f51b0f638108bd075c08e6d6707e0c0387c0b
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In Algebra and Number Theory
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In Statistical and Nonlinear Physics
Citations in the corpus
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces. I. General theory (2012, background): “Ocneanu’s pioneering work in the subfactor context [26], and more recent developments in the purely algebraic framework [1, 27, 12]).”