On module categories over finite-dimensional Hopf algebras

NICOLÁS ANDRUSKIEWITSCH; MARTÍN MOMBELLI

JOURNAL OF ALGEBRA

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2007 p. 383 - 418

0021-8693

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 equivariantMorita 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).