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Communications in Algebra Volume 50, 2022 - Issue 5
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On the length of the group algebra of the dihedral group in the semi-simple case

Michael A. Khrystika Department of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, RussiaView further author information
&
Olga V. Markovaa Department of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, Russia;b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia;c Moscow Institute of Physics and Technology (State University), Dolgoprudny, RussiaCorrespondence[email protected]
View further author information
Pages 2223-2232 | Received 25 Jul 2020, Accepted 04 Nov 2021, Published online: 29 Nov 2021
 
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Abstract

The length of group algebras for the dihedral groups is calculated in the semi-simple case. For arbitrary n > 2, we prove that the length of the group algebra of the dihedral group of order 2n over an arbitrary field of a characteristic not dividing 2n is equal to n.

2020 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgment

The authors are grateful to Prof. A.E. Guterman for valuable comments and suggestions during the preparation of the paper and to the referee for numerous useful suggestions substantially improving the paper.

Additional information

Funding

This research is financially supported by Russian Science Foundation grant 17-11-01124.

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