2-Local Automorphisms on Basic Classical Lie Superalgebras  

作　　者：Li YU Ying WANG Hai Xian CHEN Ji Zhu NAN 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology [2]School of Mathematical Sciences, Shanxi University

出　　处：《Acta Mathematica Sinica,English Series》2019年第3期427-437,共11页数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11471090)

摘　　要：Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).

关 键 词：Basic CLASSICAL LIE SUPERALGEBRA 2-local AUTOMORPHISM AUTOMORPHISM 

分 类 号：O1[理学—数学]