On some "minimal" Leibniz algebras

被引：17

作者：

Chupordia, V. A. ^{[1
]}

Kurdachenko, L. A. ^{[1
]}

Subbotin, I. Ya. ^{[2
]}

机构：

[1] Dnepropetrovsk Natl Univ, Dept Geometry & Algebra, 72 Gagarin Av, UA-49010 Dnepropetrovsk, Ukraine

[2] Natl Univ, Dept Math & Nat Sci, 5245 Pacific Concourse Dr, Los Angeles, CA 90045 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2017年 / 16卷 / 05期

关键词：

Leibniz algebra; Lie algebra; cyclic subalgebra; left center; right center; center of Leibniz algebra; nilpotent subalgebras; abelian subalgebras; LIE-ALGEBRAS; HOMOLOGY;

D O I：

10.1142/S0219498817500827

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to describe some "minimal" Leibniz algebras, that are the Leibniz algebras whose proper subalgebras are Lie algebras, and the Leibniz algebras whose proper subalgebras are abelian.

引用

页数：16

共 16 条

[1]

Bloh A., 1965, Dokl. Akad. Nauk SSSR, V165, P471

[2]

Bloh A. M., 1967, DOKL AKAD NAUK SSSR, V175, P824

[3]

Bloh A.M., 1971, Moskov. Gos. Ped. Inst. Uchen. Zap., V375, P9

[4]

Butterfield J., 1999, PHYS PHILOS

[5] Ten-term exact sequence of Leibniz homology [J].

Casas, JM ;

Pirashvili, T .

JOURNAL OF ALGEBRA, 2000, 231 (01) :258-264

[6]

Dobrev V., 2013, LIE THEORY ITS APPL

[7]

Duplij S., 2001, NONCOMMUTATIVE STRUC

[8] ON THE STRUCTURE OF SIMPLE-SEMIABELIAN LIE-ALGEBRAS [J].

FARNSTEINER, R .

PACIFIC JOURNAL OF MATHEMATICS, 1984, 111 (02) :287-299

[9] Leibniz homology of dialgebras of matrices [J].

Frabetti, A .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 129 (02) :123-141

[10]

Gein A. G., 1972, MATEM ZAP URALSK U, V8, P18

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