Complete Lie algebras with maximal-rank nilpotent radicals |
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Authors: | Linsheng Zhu Daoji Meng |
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Institution: | (1) Department of Mathematics, Changshu College, 215500 Changshu, China;(2) Department of Mathematics, Nankai University, 300071 Tianjin, China |
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Abstract: | Complete Lie algebras with maximal-rank nilpotent radicals are constructed by using the representation theory of complex semisimple
Lie algebras. A structure theorem and an isomorphism theorem for this kind of complete Lie algebras are obtained. As an application
of these theorems, the complete Lie algebras with abelian nilpotont radicals are classified. At last, it is proved that there
exists no complete Lie algebra whose radical is a nilpotent Lie algebra with maximal rank. |
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Keywords: | complete Lie algebra nilpotent Lie algebra with maximal rank irreducible module |
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