Group algebras with units satisfying a group identity

Chia Hsin Liu

doi:10.1090/s0002-9939-99-04744-9

Group algebras with units satisfying a group identity

Chia Hsin Liu^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

Abstract

Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

Original language	English
Pages (from-to)	327-336
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9939-99-04744-9
Publication status	Published - 1999
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-99-04744-9

Cite this

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AB - Let K[G] be the group algebra of a group G over a field K, and let U(K[G]) be its group of units. A conjecture by Brian Hartley asserts that if G is a torsion group and U(K[G]) satisfies a group identity, then K[G] satisfies a polynomial identity. This was verified earlier in case K is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

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Group algebras with units satisfying a group identity

Abstract

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