Representations of Classical Lie Algebras from their Quantum Deformations

Details Representations of Classical Lie Algebras from their Quantum Deformations Representations of Classical Lie Algebras from their Quantum Deformations

2004-07-23

arxiv.org/abs/math-ph/0407055v1

Inst. Phys. conf. Ser. No 173: Section 8, Paper presented at 24th Int. Coll. Group Theoretical Methods in Physics, Paris, Fran

Physics

Mathematical Physics

Scientific paper

We make use of a well-know deformation of the Poincar\'e Lie algebra in $p+q+1$ dimensions ($p+q>0$) to construct the Poincar\'e Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the Poincar\'e Lie algebra appearing as certain irrational functions of the generators of the de Sitter groups. We have obtained generalizations of this ``anti-deformation'' for the $SO(p+2,q)$ and $SO(p+1,q+1)$ cases with arbitrary $p$ and $q$. Similar results have been established for $q$ deformations $U_q(so(p,q))$ with small $p$ and $q$ values. Combining known results on representations of $U_q(so(p,q))$ (for $q$ both generic and a root of unity) with our ``anti-deformation'' formulae, we get representations of classical Lie algebras which depend upon the deformation parameter $q$. Explicit results are given for the simplest example (of type $A_1$) i.e. that associated with $U_q(so(2,1))$.

Affiliated with

Also associated with

No associations

Rating

Representations of Classical Lie Algebras from their Quantum Deformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of Classical Lie Algebras from their Quantum Deformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of Classical Lie Algebras from their Quantum Deformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246474