International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 72, Pages 4539-4545
doi:10.1155/S016117120320908X

On the Steenrod operations in cyclic cohomology

Mohamed Elhamdadi1 and Yasien Gh. Gouda2

1Department of Mathematics, University of South Florida, Tampa 33620, FL, USA
2Department of Mathematics, Faculty of Science, South Valley University, Aswan, Egypt

Received 12 September 2002

Copyright © 2003 Mohamed Elhamdadi and Yasien Gh. Gouda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For a commutative Hopf algebra A over ℤ/p, where p is a prime integer, we define the Steenrod operations pi in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group Sn and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations.