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The Tate-Hochschild cohomology ring of a group algebra by Nguyen, Van C. is a scholarly article available to read on EtoBox.

What is The Tate-Hochschild cohomology ring of a group algebra about?

We show that the Tate-Hochschild cohomology ring $HH^*(RG,RG)$ of a finite group algebra $RG$ is isomorphic to a direct sum of the Tate cohomology rings of the centralizers of conjugacy class representatives of $G$. Moreover, our main result provides an explicit formula for the cup product in $HH^*(RG,RG)$ with respect to this decomposition. As an example, this formula helps us to compute the Tate-Hochschild cohomology ring of the symmetric group $S_3$ with coefficients in a field of characteristic 3.

Author

Nguyen, Van C.

Published

2012

Language

EN