Cohomology algebras of blocks of finite groups and Brauer correspondence. (Q865038)

Let \(G\) be a finite group, \(k\) an algebraically closed field of characteristic \(p\), \(b\) a block of \(kG\), and let \(D_\gamma\) be a defect pointed group of \(b\). Denote by \(H^*(G,b,D_\gamma)\) Linckelmann's cohomology algebra of \(b\). Assume that a subgroup \(H\) of \(G\) normalizes a subgroup \(Q\) of \(D\) and \(D\) contains \(QC_G(Q)\). Let \(c\) be a block of \(kH\) such that \(b=c^G\) in the sense of Brauer. Then there is an inclusion \(H^*(G,b,D_\gamma)\subseteq H^*(H,c,D_\delta)\). In this paper, the authors show that under certain conditions, the \(kHc\)-\(kGb\)-bimodule \(ckGb\) induce a transfer map from \(H^*(H,c,D_\delta)\) to \(H^*(G,b,D_\gamma)\), and investigate the properties of this map.