On the lengths of group algebras of finite abelian groups in the semi-simple case

Alexander Guterman; Olga Markova; Mikhail Khrystik

doi:10.1142/s0219498822501407

On the lengths of group algebras of finite abelian groups in the semi-simple case

Alexander Guterman
, Olga Markova
, Mikhail Khrystik

Moscow Center for Fundamental and Applied Mathematics
Moscow Institute of Physics and Technology
Lomonosov Moscow State University

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

8 Scopus citations

Abstract

In this paper we solve the problem of finding the length of group algebras of arbitrary finite abelian groups in the case when the characteristic of the ground field does not divide the order of the group. We show that these group algebras have maximal possible lengths for infinite fields and sufficiently large finite fields since they are one-generated. In case of small fields we prove that the length is bounded from above by a logarithmic function of the order of the group.

Original language	English
Article number	2250140
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	7
DOIs	https://doi.org/10.1142/s0219498822501407
State	Published - 1 Jul 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Funding

The authors are grateful to A. A. Klyachko for the important suggestions on this paper and to the referee for numerous useful comments substantially improving the paper. The investigations of the first and the second authors are supported by Russian Science Foundation Grant 17-11-01124.

Funders	Funder number
Russian Science Foundation	17-11-01124

Keywords

Finite-dimensional algebras
abelian groups
group algebras
lengths of sets and algebras

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10.1142/s0219498822501407

Cite this

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KW - lengths of sets and algebras

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On the lengths of group algebras of finite abelian groups in the semi-simple case

Abstract

Bibliographical note

Funding

Keywords

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