Vol. 2, No. 5, 2008

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Homology and cohomology of quantum complete intersections

Petter Andreas Bergh and Karin Erdmann

Vol. 2 (2008), No. 5, 501–522
Abstract

We construct a minimal projective bimodule resolution for every finite-dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In particular, we show that the cohomology vanishes in high degrees, while the homology is always nonzero.

Keywords
quantum complete intersection, Hochschild cohomology, Hochschild homology
Mathematical Subject Classification 2000
Primary: 16E40
Secondary: 81R50, 16U80, 16S80
Milestones
Received: 15 October 2007
Revised: 29 May 2008
Accepted: 7 June 2008
Published: 4 July 2008
Authors
Petter Andreas Bergh
Institutt for matematiske fag
NTNU
N-7491 Trondheim
Norway
http://www.math.ntnu.no/~bergh
Karin Erdmann
Mathematical Institute
24-29 St. Giles
Oxford
OX1 3LB
United Kingdom
http://www.maths.ox.ac.uk/~erdmann