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Algèbres de Lie rigides

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Goze, Michel and Ancochea Bermúdez , José María (1985) Algèbres de Lie rigides. Indagationes Mathematicae, 47 (4). pp. 397-415. ISSN 0019-3577



Abstract

The goal in this article is to give a constructive method describing the n-dimensional rigid Lie algebras μ, with "rigid'' meaning, in the simplest sense, that every Lie algebra law sufficiently close to μ is isomorphic to it. The authors use Lie algebra results obtained by Goze via methods of nonstandard analysis, as well as the following theorem, due to R. Carles : For a law μ in Cn to be rigid, it must possess a semisimple inner derivation with integer eigenvalues. This reduces the problem to the study of a system of roots associated with this adjoint: Various nonrigidity criteria are given by properties of the system. The authors are then able to describe rigid laws both in arbitrary and in small dimensions; an example in C6 is completely illustrated and the 31 solvable rigid laws of dimension 8 are described


Item Type:Article
Uncontrolled Keywords:rigid Lie algebras; solvable Lie algebras of dimension eight; nonstandard method; cohomology
Subjects:Sciences > Mathematics > Algebra
ID Code:21271
Deposited On:08 May 2013 14:35
Last Modified:12 Dec 2018 15:14

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