Tensor Products and Support Varieties for Some Noncocommutative Hopf Algebras
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.
KeywordsProjective modules Nonsemisimple Hopf algebra Support varieties Smash coproduct
Mathematics Subject Classification (2010)16T05 18D10
Unable to display preview. Download preview PDF.
- 3.Bakalov, B., Kirillov A. Jr.: Lectures on Tensor Categories and Modular Functors. Volume 21 of University Lecture Series. American Mathematical Society, Providence, RI (2001)Google Scholar
- 4.Benson, D.: Representations and Cohomology II: Cohomology of Groups and Modules. volume 31 of Cambridge Studies in Advanced Mathematics Cambridge University Press (1991)Google Scholar
- 5.Benson, D.: Representations and Cohomology I: Basic Representation Theory of Finite Groups and Associative Algebras, volume 30 of Cambridge Studies in Advanced Mathematics Cambridge University Press (1995)Google Scholar
- 10.Karpilovsky, G.: Group Representations. Vol. 2, volume 177 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam (1993)Google Scholar
- 11.Majid, S.: More examples of bicrossproduct and double cross product Hopf algebras. Israel J. Math. Hopf algebras 72(1–2), 133–148 (1990). doi: 10.1007/BF02764616