Irreducible representations of crossed products Academic Article

abstract

• We prove that if the dimension of any irreducible module for a finite-dimensional algebra over an algebraically closed field divides the dimension of the algebra, then the same is true of any crossed product of that algebra with a group algebra or its dual, provided the characteristic of the field does not divide the order of the group. Kaplansky's Conjecture regarding dimensions of irreducible modules for Hopf algebras then follows for those finite-dimensional semisimple Hopf algebras constructed by a sequence of crossed products involving group algebras and their duals. We show that any semisimple Hopf algebra of prime power dimension in characteristic 0 is of this type, so that Kaplansky's Conjecture holds for these Hopf algebras, 1998 Elsevier Science B.V. All rights reserved.

authors

• Witherspoon, Sarah

published proceedings

• Journal of Pure and Applied Algebra

author list (cited authors)

• Montgomery, S., & Witherspoon, S. J.

citation count

• 39

complete list of authors

• Montgomery, Susan||Witherspoon, SJ

publication date

• January 1998

publisher

• Elsevier  Publisher

published in

• Journal of Pure and Applied Algebra  Journal

Digital Object Identifier (DOI)

• 10.1016/s0022-4049(97)00077-7

start page

• 315

end page

• 326

volume

• 129

issue

• 3

URL

• http://dx.doi.org/10.1016/s0022-4049(97)00077-7