2026-06-08T12:21:27Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/437852024-07-16T15:07:23Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Campoamor Stursberg, Otto-Rudwig
author
Low, S. G.
2023-06-20T03:32:18Z
2023-06-20T03:32:18Z
2009
1751-8113
10.1088/1751-8113/42/6/065205
https://hdl.handle.net/20.500.14352/43785
https//doi.org/10.1088/1751-8113/42/6/065205
http://iopscience.iop.org/1751-8121/42/6/065205/
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.
eng
Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
journal article
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https://docta.ucm.es/bitstreams/8714f2a7-5015-4d58-9564-cef3547adb65/download
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4597d692d3eaeba280859e4d3793cfc6
254540
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Campoamor-Virtual.pdf
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5eea49f7260b81816962ab73159811bb
51235
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Campoamor-Virtual.pdf.txt