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oai:docta.ucm.es:20.500.14352/437852024-07-16T15:07:23Zcom_20.500.14352_14col_20.500.14352_15

Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators Campoamor Stursberg, Otto-Rudwig Low, S. G. 512.554.3 Lie algebra Universal enveloping algebra Casimir operator Semidirect product Álgebra 1201 Álgebra 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. Ministerio de Educación, Formación Profesional y Deportes (España) Universidad Complutense de Madrid Comunidad de Madrid Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-20T03:32:18Z 2023-06-20T03:32:18Z 2009 journal article https://hdl.handle.net/20.500.14352/43785 1751-8113 10.1088/1751-8113/42/6/065205 eng MTM2006-09152 CCG07-UCM/ESP-2922 open access application/pdf IOP Publishing Ltd