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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 1982, Number 2, Pages 29–34
(Mi vmumm4151)
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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
Classification of homogeneous elements of $\mathbf{Z}_2$-graded semisimple Lie algebras
L. V. Antonyan
Abstract:
Let $\mathfrak{g}=\mathfrak{g}_0\oplus\mathfrak{g}_1$ be a $\mathbf{Z}_2$-graded semisimple Lie algebra over the complex number field. Our purpose is threefold. First, we describe the conjugacy classes of $\mathfrak{g}$ that intersect $\mathfrak{g}_1$. Second, we show that all classes intersect $\mathfrak{g}_1$ if and only if $\mathfrak{g}_1$ contains a Cartan subalgebra of $\mathfrak{g}$. Third, we obtain some necessary and sufficient conditions, under which all classes of nilpotent elements in $\mathfrak{g}$ intersect $\mathfrak{g}_1$.
Received: 23.09.1981
Citation:
L. V. Antonyan, “Classification of homogeneous elements of $\mathbf{Z}_2$-graded semisimple Lie algebras”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, no. 2, 29–34
Linking options:
https://www.mathnet.ru/eng/vmumm4151 https://www.mathnet.ru/eng/vmumm/y1982/i2/p29
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