RT Journal Article
T1 The structure of the invariants of perfect Lie algebras
A1 Campoamor Stursberg, Otto-Rudwig
AB 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 ofsubalgebras 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.
PB IOP Publishing
SN 0305-4470
YR 2003
FD 2003
LK https://hdl.handle.net/20.500.14352/50701
UL https://hdl.handle.net/20.500.14352/50701
LA eng
NO Fondation Ramón Areces
DS Docta Complutense
RD 21 abr 2025