Strong contraction of the representations of the three-dimensional Lie algebras

For any nönü-Wigner contraction of a three-dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-07, Vol.45 (26), p.265206-25
Main Authors: Subag, E M, Baruch, E M, Birman, J L, Mann, A
Format: Article
Language:English
Subjects:
Construction contracts
Contracts
Exact sciences and technology
Functions (mathematics)
Lie groups
Mathematical analysis
Operators
Physics
Proving
Representations
Three dimensional
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For any nönü-Wigner contraction of a three-dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/26/265206