Algebra & Number Theory

Finite generation of the cohomology of some skew group algebras

Van Nguyen and Sarah Witherspoon

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Abstract

We prove that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens’ proof of finite generation of group cohomology. We apply the result to a series of examples of finite-dimensional Hopf algebras in positive characteristic.

Article information

Source
Algebra Number Theory, Volume 8, Number 7 (2014), 1647-1657.

Dates
Received: 4 October 2013
Accepted: 17 August 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730270

Digital Object Identifier
doi:10.2140/ant.2014.8.1647

Mathematical Reviews number (MathSciNet)
MR3272277

Zentralblatt MATH identifier
1304.16014

Subjects
Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05]

Keywords
cohomology Hopf algebras skew group algebras

Citation

Nguyen, Van; Witherspoon, Sarah. Finite generation of the cohomology of some skew group algebras. Algebra Number Theory 8 (2014), no. 7, 1647--1657. doi:10.2140/ant.2014.8.1647. https://projecteuclid.org/euclid.ant/1513730270


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Corrections

  • Van C. Nguyen, Sarah Witherspoon. Correction to the article Finite generation of the cohomology of some skew group algebras. Algebra Number Theory 12 (2018), no. 2, 491--492.