Local Automorphisms on Finite-Dimensional Lie and Leibniz Algebras

被引：5

作者：

Ayupov, Shavkat ^{[1
]}

Kudaybergenov, Karimbergen ^{[2
]}

机构：

[1] Uzbek Acad Sci, VI Romanovskiy Inst Math, 81 Mirzo Ulughbek St, Tashkent 100170, Uzbekistan

[2] Karakalpak State Univ, Dept Math, Ch Abdirov 1, Nukus 230113, Uzbekistan

来源：

ALGEBRA, COMPLEX ANALYSIS, AND PLURIPOTENTIAL THEORY | 2018年 / 264卷

关键词：

Simple Lie algebra; Simple Leibniz algebra; Nilpotent Lie algebra; Automorphism; Local automorphism; 2-LOCAL DERIVATIONS;

D O I：

10.1007/978-3-030-01144-4_3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a linear mapping on the algebra sl(n) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an antiautomorphism. We also show that a linear mapping on a simple Leibniz algebra of the form sl(n)+-J , is a local automorphism if and only if it is an automorphism. We give examples of finite-dimensional nilpotent Lie algebras I with dim I >= 3 which admit local automorphisms which are not automorphisms.

引用

页码：31 / 44

页数：14

共 21 条

[11] 2-Local automorphisms of finite-dimensional simple Lie algebras [J].

Chen, Zhengxin ;

Wang, Dengyin .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 486 :335-344

[12] Nonlinear maps satisfying derivability on standard parabolic subalgebras of finite-dimensional simple Lie algebras [J].

Chen, Zhengxin ;

Wang, Dengyin .

LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (03) :261-270

[13]

Humphreys J.E., 1972, INTRO LIE ALGEBRAS R

[14] LOCAL DERIVATIONS [J].

KADISON, RV .

JOURNAL OF ALGEBRA, 1990, 130 (02) :494-509

[15] Local automorphisms and derivations on Mn [J].

Kim, SO ;

Kim, JS .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (05) :1389-1392

[16]

Larson D. R., 1990, P S PURE MATH 2, P187, DOI DOI 10.1090/PSPUM/051.2/1077437

[17]

Molnar L., 2007, Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, V1895

[18] LINEAR MAPPINGS PRESERVING SQUARE-ZERO MATRICES [J].

SEMRL, P .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1993, 48 (03) :365-370

[19] Local automorphisms and derivations on beta(H) [J].

Semrl, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (09) :2677-2680

[20]

VERGNE M, 1966, CR ACAD SCI A MATH, V263, P4

← 1 2 3 →