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Automorphism groups of axial algebras Научная публикация

Журнал

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Вых. Данные

Год: 2025, Том: 661, Страницы: 657-712 Страниц : 56 DOI: 10.1016/j.jalgebra.2024.08.007

Ключевые слова

Axial algebra, Non-associative algebra, Monster, Jordan algebra, Automorphism, Automorphism group, Idempotent, Computational algebra

Авторы

Gorshkov I.B. ¹ , McInroy J. ^2,3 , Mudziiri Shumba T.M. ¹ , Shpectorov S. ⁴

Организации

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

Информация о финансировании (2)

1	Министерство науки и высшего образования РФ Математический центр в Академгородке	075-15-2019-1613, 075-15-2022-281
2	Математический центр в Академгородке	075-15-2019-1675

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.

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 OpenAlex

Поступила в редакцию:	19 февр. 2024 г.
Опубликована online:	22 авг. 2024 г.
Опубликована в печати:	1 янв. 2025 г.

Web of science:	WOS:001304328700001
Scopus:	2-s2.0-85202694708
OpenAlex:	W4401831604

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