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Bulletin of the London Mathematical Society Advance Access originally published online on March 22, 2009
Bulletin of the London Mathematical Society 2009 41(3):473-482; doi:10.1112/blms/bdp018
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© 2009 London Mathematical Society

Hochschild homology and global dimension

Petter Andreas Bergh and Dag Madsen

Institutt for Matematiske fag
NTNU
7491 Trondheim
Norway
dagma@math.ntnu.no

Received 31 March 2008. Revision received 28 August 2008.

We prove that, for certain classes of graded algebras (Koszul, local and cellular), infinite global dimension implies that Hochschild homology does not vanish in high degrees, provided that the characteristic of the ground field is zero. Our proof uses Igusa's formula relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant.

2000 Mathematics Subject Classification 16E40, 16W50.

The authors were supported by NFR Storforsk grant no. 167130.


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