Hochschild homology and global dimension
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Thu, 16/10/2008 14:30 |
Petter Bergh (Trondheim / Oxford) |
Representation Theory Seminar  |
L3 |
| In 1989, Happel raised the following question: if the Hochschild cohomology groups of a finite dimensional algebra vanish in high degrees, then does the algebra have finite global dimension? This was answered negatively in a paper by Buchweitz, Green, Madsen and Solberg. However, the Hochschild homology version of Happel's question, a conjecture given by Han, is open. We give a positive answer to this conjecture for local graded algebras, Koszul algebras and cellular algebras. The proof uses Igusa's formula for relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant. This is joint work with Dag Madsen. | |||