On the theta completions for maximal subalgebras |
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Authors: | Leila Goudarzi |
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Affiliation: | 1. Department of Mathematics, University of Ayatollah Alozma Boroujerdi, Boroujerd, Iranle.goudarzi@abru.ac.ir |
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Abstract: | Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and ML?C and C∕ML contains no non-zero ideal of L∕ML, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra. |
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Keywords: | 𝜃 -Completion Lie algebra nilpotent solvable strong 𝜃 -completion |
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