2-Local Automorphisms on Basic Classical Lie Superalgebras |
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Authors: | Li Yu Ying Wang Hai Xian Chen Ji Zhu Nan |
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Institution: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China;2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P. R. China |
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Abstract: | 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). |
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Keywords: | Basic classical Lie superalgebra 2-local automorphism automorphism |
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