New York Journal of Mathematics
Volume 23 (2017) 351-364


Jon F. Carlson and Srikanth B. Iyengar

Hopf algebra structures and tensor products for group algebras

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Published: March 15, 2017
Keywords: Coproduct, elementary abelian group, Hochschild cohomology, Hopf algebra, tensor product of modules
Subject: 20J06 (primary), 20C20

The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of a commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures that determine cup products on cohomology of modules. However, it is proved in this paper that the products with elements of the polynomial subring of the cohomology ring generated by the Bocksteins of the degree one elements are independent of the choice of these coalgebra structures.


JFC was partially supported by NSA grant H98230-15-1-0007 and by Simons Foundation grant 054813-01. SBI was partially supported by NSF grant DMS-1503044. JFC would like to thank the University of Utah for kind hospitality during his visit when the work on this paper was started.

Author information

Jon F. Carlson:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA

Srikanth B. Iyengar:
Department of Mathematics, University of Utah, Salt Lake City, UT 68588, USA