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Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

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Campoamor Stursberg, Otto Ruttwig and Low, S.G. (2009) Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators. Journal of physics A: Mathematical and theoretical, 42 (6). pp. 1-18. ISSN 1751-8113

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Official URL: http://iopscience.iop.org/1751-8121/42/6/065205/


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Abstract

Given a semidirect product g = s ⊎ r of semisimple Lie algebras s and solvable algebras r, we construct polynomial operators in the enveloping algebra U(g) of g that commute with r and transform like the generators of s, up to a functional factor that turns out to be a Casimir operator of r. Such operators are said to generate a virtual copy of s in U(g), and allow to compute the Casimir operators of g in closed form, using the classical formulae for the invariants of s. The behavior of virtual copies
with respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given.


Item Type:Article
Uncontrolled Keywords:Lie algebra; universal enveloping algebra; Casimir operator; semidirect product
Subjects:Sciences > Mathematics > Algebra
ID Code:21120
Deposited On:29 Apr 2013 16:23
Last Modified:12 Dec 2018 15:13

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