2026-06-27T23:20:51Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/507012024-07-16T15:15:25Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Campoamor Stursberg, Otto-Rudwig
2023-06-20T10:35:42Z
2023-06-20T10:35:42Z
2003
0305-4470
https://hdl.handle.net/20.500.14352/50701
http://iopscience.iop.org/0305-4470/36/24/309/pdf/0305-4470_36_24_309.pdf
http://iopscience.iop.org/
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.
eng
The structure of the invariants of perfect Lie algebras
journal article
URL
https://docta.ucm.es/bitstreams/5a1b8a82-7573-425c-bf62-411a43519afe/download
File
MD5
821a94e9c75af0f18bf713e028a550c2
196240
application/pdf
Campoamor-The_structure.pdf