NONSTANDARD QUANTUM SO(2,2) AND BEYOND

Citation
A. Ballesteros et al., NONSTANDARD QUANTUM SO(2,2) AND BEYOND, Journal of physics. A, mathematical and general, 28(4), 1995, pp. 941-955
Citations number
21
Categorie Soggetti
Physics
ISSN journal
03054470
Volume
28
Issue
4
Year of publication
1995
Pages
941 - 955
Database
ISI
SICI code
0305-4470(1995)28:4<941:NQSAB>2.0.ZU;2-P
Abstract
A new 'non-standard' quantization of the universal enveloping algebra of the split (natural) real form so(2, 2) of D-2 is presented. Some (c lassical) graded contractions of so(2, 2) associated to a Z(2) x Z(2) grading are studied, and the automorphisms defining this grading are g eneralized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of 'non-standard' quantum al gebras; Some of these algebras can be realized as (2 + 1) kinematical algebras; we explicitly introduce a new deformation of Poincare algebr a, which is naturally linked to the null plane basis. Another realizat ion of these quantum algebras as deformations of the conformal algebra s for the two-dimensional Euclidean, Galilei and Minkowski spaces is g iven, and its new properties are emphasized.