Casimir operators induced by the Maurer–Cartan equations

DOI10.1088/1751-8113/41/36/365207zbMATH Open1149.17005arXiv0805.2982OpenAlexW3105082182WikidataQ58324991 ScholiaQ58324991MaRDI QIDQ3526030

Rutwig Campoamor Stursberg

Publication date: 24 September 2008

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: It is shown that for inhomogeneous Lie algebras

f r a k g = f r a k s o v e r r i g h t a r r o w {o p l u s}_{L a m b d a} (d i m L a m b d a) L_{1}

satisfying the condition

m a t h c a l N (f r a k g) = 1

, the only Casimir operator can be explicitly constructed from the Maurer-Cartan equations by means of wedge products. It is shown that this constraint imposes sharp bounds for the dimension of the representation

R

. The procedure is generalized to compute also the rational invariant of some Lie algebras.

Full work available at URL: https://arxiv.org/abs/0805.2982

zbMATH Keywords

Lie algebra Casimir operator

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Solvable, nilpotent (super)algebras (17B30)