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The structure of the invariants of perfect Lie algebras

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Campoamor Stursberg, Otto Ruttwig (2003) The structure of the invariants of perfect Lie algebras. Journal of physics A: Mathematical and general, 36 (24). pp. 6709-6723. ISSN 0305-4470

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Official URL: http://iopscience.iop.org/0305-4470/36/24/309/pdf/0305-4470_36_24_309.pdf


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Abstract

Upper bounds for the number N(g) of Casimir operators of perfect Lie algebras g with nontrivial Levi decomposition are obtained, and in particular the existence of nontrivial invariants is proved. It is shown that for high-ranked representations R the Casimir operators of the semidirect sum s −→⊕ R(deg R)L1 of a semisimple Lie algebra s and an Abelian Lie algebra (deg R)L1 of dimension equal to the degree of R are completely determined by the representation R, which also allows the analysis of the invariants of
subalgebras which extend to operators of the total algebra. In particular, for the adjoint representation of a semisimple Lie algebra the Casimir operators of s −→⊕ ad(s)(dims)L1 can be explicitly constructed from the Casimir operators of the Levi part s.


Item Type:Article
Subjects:Sciences > Mathematics > Algebra
ID Code:21778
Deposited On:11 Jun 2013 12:50
Last Modified:12 Dec 2018 15:13

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