Axial algebras of Monster type (2η,η) for D diagrams. I | Sciact - Система учета научной деятельности ИМ СО РАН

Axial algebras of Monster type (2η,η) for D diagrams. I Научная публикация

Журнал

Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125

Вых. Данные

Год: 2025, Том: 53, Номер: 8, Страницы: 3218-3252 Страниц : 35 DOI: 10.1080/00927872.2025.2457010

Ключевые слова

Axial algebra; Matsuo algebra; double axis; 3-transpostion group

Авторы

Mamontov Andrey ¹ , Staroletov Alexey ¹

Организации

1	Sobolev Institute of Mathematics

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0002

Axial algebras are a class of commutative algebras generated by idempotents with adjoint action semisimple and satisfying a prescribed fusion law. The class of Matsuo algebras was introduced by Matsuo and later generalized by Hall, Rehren, and Shpectorov. A Matsuo algebra M is built by a set of 3-transpositions D. Elements of D are idempotents in M and called axes. It is known that double axes, i.e., sums of two orthogonal axes in a Matsuo algebra, satisfy the fusion law of Monster type. In this paper, we study primitive subalgebras generated by a single axis and two double axes. We classify all such subalgebras in seven out of nine possible cases for a diagram on 3-transpositions that are involved in the generating elements. We also construct several infinite series of axial algebras of Monster type generalizing our 3-generated algebras.

Mamontov A. , Staroletov A.
Axial algebras of Monster type (2η,η) for D diagrams. I
Communications in Algebra. 2025. Т.53. №8. С.3218-3252. DOI: 10.1080/00927872.2025.2457010 WOS Scopus OpenAlex

Поступила в редакцию:	5 янв. 2023 г.
Принята к публикации:	14 янв. 2025 г.
Опубликована online:	7 февр. 2025 г.

Web of science:	WOS:001467505300001
Scopus:	2-s2.0-85217577188
OpenAlex:	W4407251770

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