Non-semisimple Lie algebras with Levi factor so(3), sl(2,R) and their invariants

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Campoamor Stursberg, Otto Ruttwig (2003) Non-semisimple Lie algebras with Levi factor so(3), sl(2,R) and their invariants. Journal of physics A: Mathematical and general, 36 (5). pp. 1357-1369. ISSN 0305-4470

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Official URL: http://arxiv.org/pdf/math/0208195v1.pdf




Abstract

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0


Item Type:Article
Subjects:Sciences > Mathematics > Algebra
ID Code:22031
Deposited On:20 Jun 2013 14:57
Last Modified:12 Dec 2018 15:13

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