The Hochschild cohomology ring of a cyclic block 
by Stephen F. Siegel, and Sarah J. Witherspoon 

March 13, 1998 

        Abstract. Suppose $B$ is a block of a group algebra $kG$ with cyclic 
defect group. We calculate the Hochschild cohomology ring of $B$, giving a
complete set of generators and relations. We then show that if $B$ is the 
principal block, the canonical map from $H^*(G,k)$ to the Hochschild
cohomology ring of $B$ induces an isomorphism modulo radicals.