On graded centres and block cohomology

Linckelmann, M. (2009). On graded centres and block cohomology. Proceedings of the Edinburgh Mathematical Society, 52(2), pp. 489-514. doi: 10.1017/S0013091507001137

Abstract

We extend the group theoretic notions of transfer and stable elements to graded centers of triangulated categories. When applied to the center H∗Db(B)) of the derived bounded category of a block algebra B we show that the block cohomology H∗(B) is isomorphic to a quotient of a certain subalgebra of stable elements of H∗(Db(B)) by some nilpotent ideal, and that a quotient of H∗(Db(B)) by some nilpotent ideal is Noetherian over H∗(B).