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Algebras and Representation Theory

, Volume 21, Issue 2, pp 259–276 | Cite as

Tensor Products and Support Varieties for Some Noncocommutative Hopf Algebras

  • Julia Yael Plavnik
  • Sarah Witherspoon
Article

Abstract

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor powers of nonprojective modules are projective and tensor products of modules in one order are projective but in the other order are not. Our examples are smash coproducts with duals of group algebras, some having algebra and coalgebra structures twisted by cocycles. We apply support variety theory for these Hopf algebras as a tool in our investigations.

Keywords

Projective modules Nonsemisimple Hopf algebra Support varieties Smash coproduct 

Mathematics Subject Classification (2010)

16T05 18D10 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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