RT Journal Article
T1 Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
A1 Campoamor Stursberg, Otto-Rudwig
A1 Low, S. G.
AB 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 copieswith respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given.
PB IOP Publishing Ltd
SN 1751-8113
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/43785
UL https://hdl.handle.net/20.500.14352/43785
LA eng
NO Ministerio de Educación, Formación Profesional y Deportes (España)
NO Universidad Complutense de Madrid
NO Comunidad de Madrid
DS Docta Complutense
RD 11 abr 2025