On simple left-symmetric algebras | Sciact - Система учета научной деятельности ИМ СО РАН

On simple left-symmetric algebras Научная публикация

Журнал

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

Вых. Данные

Год: 2023, Том: 621, Страницы: 58-86 Страниц : 29 DOI: 10.1016/j.jalgebra.2023.01.009

Ключевые слова

Left-symmetric algebra; Lie-solvable algebra; Nilpotent algebra; Novikov algebra;Pre-Lie algebraSimple algebra;

Авторы

Pozhidaev A. ¹ , Umirbaev U. ^2,3,4 , Zhelyabin V. ¹

Организации

1	Sobolev Institute of Mathematics of SB RAS, Novosibirsk, Russian Federation
2	Wayne State University, Detroit, MI, United States
3	Al-Farabi Kazakh National University, Almaty, Kazakhstan
4	Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Информация о финансировании (1)

Российский научный фонд

21-11-00286

We prove that the multiplication algebra M(A) of any simple finite-dimensional left-symmetric nonassociative algebra A over a field of characteristic zero coincides with the right multiplication algebra R(A). In particular, A does not contain any proper right ideal. These results immediately give a description of simple finite-dimensional Novikov algebras over an algebraically closed field of characteristic zero [29]. The structure of finite-dimensional simple left-symmetric nonassociative algebras from a very narrow class A of algebras with the identities [[x,y],[z,t]]=[x,y]([z,t]u)=0 is studied in detail. We prove that every such algebra A admits a Z2-grading A=A0⊕A1 with an associative and commutative A0. Simple algebras are described in the following cases: (1) A is four dimensional over an algebraically closed field of characteristic not 2, (2) A0 is an algebra with the zero product, and (3) A0 is simple; in the last two cases, the description is given in terms of root systems. A necessary and sufficient condition for A to be complete is given. © 2023 Elsevier Inc.

Pozhidaev A. , Umirbaev U. , Zhelyabin V.
On simple left-symmetric algebras
Journal of Algebra. 2023. V.621. P.58-86. DOI: 10.1016/j.jalgebra.2023.01.009 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	30 авг. 2022 г.
Опубликована online:	24 янв. 2023 г.
Опубликована в печати:	9 февр. 2023 г.

Web of science:	WOS:000944733300001
Scopus:	2-s2.0-85147577840
РИНЦ:	60461665
OpenAlex:	W4317929715

БД	Цитирований
Web of science	2
OpenAlex	3
РИНЦ	5
Scopus	2