Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 5 (2008), 501-522.
Homology and cohomology of quantum complete intersections
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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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. https://projecteuclid.org/euclid.ant/1513797286