Classification of real simple Lie superalgebras of classical type
Classification of real simple Lie superalgebras of classical type
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DOI：
10.1063/1.524487
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发表时间：
1980-04
影响因子：
1.3
通讯作者：
M. Parker
中科院分区：
文献类型：
--
作者：
M. Parker
特征为零的代数闭域上的有限维单李超代数（也称为Z2阶化李代数）在1976年被分类。所有实上的单李超代数，其李子代数是约化的，在这里被确定为同构。与单李代数的理论一样，这是通过对复李超代数的对合半态进行分类来完成的。人们特别看到，李子代数的真实的形式完全决定了李超代数的真实的形式。
Finite‐dimensional simple Lie superalgebras (also called Z2‐graded Lie algebras) over an algebraically closed field of characteristic zero were classified in 1976. All simple Lie superalgebras over the reals, whose Lie subalgebra is reductive, are determined here up to isomorphism. As is the theory of simple Lie algebras, this is done by classifying the involutive semimorphisms of the complex Lie superalgebras. One sees in particular that the real form of the Lie subalgebra completely determines the real form of the Lie superalgebra.