Kyoto Journal of Mathematics

Virtual Gorensteinness over group algebras

Abdolnaser Bahlekeh and Shokrollah Salarian

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Abstract

Let Γ be a finite group, and let Λ be any Artin algebra. It is shown that the group algebra ΛΓ is virtually Gorenstein if and only if ΛΓ' is virtually Gorenstein, for all elementary abelian subgroups Γ' of Γ. We also extend this result to cover the more general context. Precisely, assume that Γ is a group in Kropholler’s hierarchy HF, Γ' is a subgroup of Γ of finite index, and R is any ring with identity. It is proved that, in certain circumstances, that RΓ is virtually Gorenstein if and only if RΓ' is so.

Article information

Source
Kyoto J. Math., Volume 55, Number 1 (2015), 129-141.

Dates
First available in Project Euclid: 13 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1426252132

Digital Object Identifier
doi:10.1215/21562261-2848133

Mathematical Reviews number (MathSciNet)
MR3323529

Zentralblatt MATH identifier
1329.16010

Subjects
Primary: 20J05: Homological methods in group theory 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 16G10: Representations of Artinian rings 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Keywords
virtually Gorenstein algebra Moore’s condition Group algebras

Citation

Bahlekeh, Abdolnaser; Salarian, Shokrollah. Virtual Gorensteinness over group algebras. Kyoto J. Math. 55 (2015), no. 1, 129--141. doi:10.1215/21562261-2848133. https://projecteuclid.org/euclid.kjm/1426252132


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