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Proceedings of the Edinburgh Mathematical Society (1)

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On graded centres and block cohomology
Part of
- Homological methods
- Representation theory of groups
Markus Linckelmann
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 2 / June 2009

Published online by Cambridge University Press:

28 May 2009, pp. 489-514
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We extend the group theoretic notions of transfer and stable elements to graded centres of triangulated categories. When applied to the centre Z*(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 Z*(Db(B)) by some nilpotent ideal, and that a quotient of Z*(Db(B)) by some nilpotent ideal is Noetherian over H*(B).