Sciact
  • EN
  • RU

Automorphism groups of axial algebras Full article

Journal Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X
Output data Year: 2025, Volume: 661, Pages: 657-712 Pages count : 56 DOI: 10.1016/j.jalgebra.2024.08.007
Tags Axial algebra, Non-associative algebra, Monster, Jordan algebra, Automorphism, Automorphism group, Idempotent, Computational algebra
Authors Gorshkov I.B. 1 , McInroy J. 2,3 , Mudziiri Shumba T.M. 1 , Shpectorov S. 4
Affiliations
1 Sobolev Institute of Mathematics
2 Department of Mathematics, University of Chester
3 School of Mathematics, University of Bristol
4 School of Mathematics, University of Birmingham

Funding (2)

1 Министерство науки и высшего образования РФ
Mathematical Center in Akademgorodok 		075-15-2019-1613, 075-15-2022-281
2 Mathematical Center in Akademgorodok 075-15-2019-1675

Abstract: Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess algebra which has the Monster sporadic simple group as its Miyamoto group. Previously, using an expansion algorithm, about 200 examples of axial algebras in the same class as the Griess algebra have been constructed in dimensions up to about 300. In this list, we see many reoccurring dimensions which suggests that there may be some unexpected isomorphisms. Such isomorphisms can be found when the full automorphism groups of the algebras are known. Hence, in this paper, we develop methods for computing the full automorphism groups of axial algebras and apply them to a number of examples of dimensions up to 151.
Cite: Gorshkov I.B. , McInroy J. , Mudziiri Shumba T.M. , Shpectorov S.
Automorphism groups of axial algebras
Journal of Algebra. 2025. V.661. P.657-712. DOI: 10.1016/j.jalgebra.2024.08.007 WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Feb 19, 2024
Published online: Aug 22, 2024
Published print: Jan 1, 2025
Identifiers:
Web of science: WOS:001304328700001
Scopus: 2-s2.0-85202694708
Elibrary: 80686207
OpenAlex: W4401831604
Citing: Пока нет цитирований
Altmetrics: