Algebra & Number Theory

Homology and cohomology of quantum complete intersections

Petter Bergh and Karin Erdmann

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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.

Article information

Algebra Number Theory, Volume 2, Number 5 (2008), 501-522.

Received: 15 October 2007
Revised: 29 May 2008
Accepted: 7 June 2008
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37] 16U80: Generalizations of commutativity 16S80: Deformations of rings [See also 13D10, 14D15]

quantum complete intersection Hochschild cohomology Hochschild homology


Bergh, Petter; Erdmann, Karin. Homology and cohomology of quantum complete intersections. Algebra Number Theory 2 (2008), no. 5, 501--522. doi:10.2140/ant.2008.2.501.

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