| 李超代数上的不变双线性型 |
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| 引用本文： | 张知学,刘丽巧. 李超代数上的不变双线性型[J]. 数学年刊A辑(中文版), 2004, 0(2) |
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| 作者姓名： | 张知学 刘丽巧 |
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| 作者单位： | 河北大学数学与计算机学院，石家庄陆军指挥学院 河北 保定 071002，石家庄 050084 |
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| 摘 要： | 本文通过定义李超代数上的形心和零次形心来考察其性质.证明了二次李超代数(G,B)上的不变数积的集合和其形心中的可逆B-超对称元素的集合之间存在一一对应.而对实单李超代数分为两种不同的类型:或者是一个忽略了复结构的复李超代数或者是一个复单李超代数的实形式.
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| 关 键 词： | 二次李超代数 形心 复结构 |
INVARIANT BILINEAR FORMS ON LIE SUPERALGEBRAS |
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| ZHANG Zhixue LIU Liqiao'Institute of Mathematics and Computers,Hebei University,Baoding ,Hebei,China."Army Commands Academy of P.L.A.,Shijiazhuang ,China.. INVARIANT BILINEAR FORMS ON LIE SUPERALGEBRAS[J]. Chinese Annals of Mathematics, 2004, 0(2) |
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| Authors: | ZHANG Zhixue LIU Liqiao'Institute of Mathematics Computers,Hebei University,Baoding ,Hebei,China." Army Commands Academy of P.L.A.,Shijiazhuang ,China. |
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| Affiliation: | ZHANG Zhixue LIU Liqiao'Institute of Mathematics and Computers,Hebei University,Baoding 071002,Hebei,China."Army Commands Academy of P.L.A.,Shijiazhuang 050084,China. |
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| Abstract: | This paper investigates Lie supseralgebras by definning the centroid and the zero degree centroid on them. The authors prove that for a quadratic Lie superalgebra (G,B), there is a 1-1 correspondence between the set of invariant scalar products and the set of invertible B-supersymmetric elements in the centroid.At last, the authors show that the real simple Lie superalgebras are of two distinct types. Either the Lie superalgebra is really a complex Lie superalgebra with the complex structure ignored or the Lie superalgebra is a real form of a complex simple Lie superalgebra. |
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| Keywords: | Quadratic Lie superalgebra Centroid Complex structrue |
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