Casimir operators for Lie superalgebras
| dc.creator | Leites, Dimitry | |
| dc.creator | Sergeev, Alexander | |
| dc.date | 2002-02-18 | |
| dc.date.accessioned | 2026-07-07T04:46:32Z | |
| dc.date.available | 2026-07-07T04:46:32Z | |
| dc.description | Casimir operators -- the generators of the center of the enveloping algebra -- are described for simple or close to them ``classical'' finite dimensional Lie superalgebras with nondegenerate symmetric even bilinear form in Sergeev A., The invariant polynomials on simple Lie superalgebras. Represent. Theory 3 (1999), 250--280; math-RT/9810111 and for the ``queer'' series in Sergeev A., The centre of enveloping algebra for Lie superalgebra Q(n, C). Lett. Math. Phys. 7, no. 3, 1983, 177--179. Here we consider the remaining cases, and state conjectures proved for small values of parameter. Under deformation (quantization) the Poisson Lie superalgebra po(0|2n) on purely odd superspace turns into gl(2^{n-1}|2^{n-1}) and, conjecturally, the lowest terms of the Taylor series expansion with respect to the deformation parameter (Planck's constant) of the Casimir operators for gl(2^{n-1}|2^{n-1}) are the Casimir operators for po(0|2n). Similarly, quantization sends po(0|2n-1) into q(2^{n-1}) and the above procedure makes Casimir operators for q(2^{n-1}) into same for po(0|2n-1). Casimir operators for the Lie superalgebra vect(0|m) of vector fields on purely odd superspace are only constants for m>2. Conjecturally, same is true for the Lie superalgebra svect(0|m) of divergence free vector fields, and its deform, for m>3. Invariant polynomials on po(0|2n-1) are also described. They do not correspond to Casimir operators. | |
| dc.description | 4 p., Latex | |
| dc.identifier | https://arxiv.org/abs/math/0202180 | |
| dc.identifier | http://arxiv.org/abs/math/0202180 | |
| dc.identifier | E. Ivanov E. et. al. (eds.) {\it Supersymmetries and Quantum Symmetries} (SQS'99, 27--31 July, 1999), Dubna, JINR, 2000, 409--411 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63371 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B20, 17A70 (Primary) 17B35, 17B70 (Secondary) | |
| dc.title | Casimir operators for Lie superalgebras | |
| dc.type | text |