Casimir invariants for the complete family of quasi-simple orthogonal algebras
| dc.creator | Herranz, Francisco J. | |
| dc.creator | Santander, Mariano | |
| dc.date | 1997-02-24 | |
| dc.date.accessioned | 2026-07-07T10:59:01Z | |
| dc.date.available | 2026-07-07T10:59:01Z | |
| dc.description | A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given. | |
| dc.description | 19 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/physics/9702032 | |
| dc.identifier | http://arxiv.org/abs/physics/9702032 | |
| dc.identifier | J.Phys.A30:5411-5426,1997 | |
| dc.identifier | doi:10.1088/0305-4470/30/15/026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/187307 | |
| dc.subject | Mathematical Physics | |
| dc.title | Casimir invariants for the complete family of quasi-simple orthogonal algebras | |
| dc.type | text |