A definition of contraction of Lie algebra representations using direct limit

In this paper the frequently used procedures for contraction of Lie algebra representations which were introduced by Inönü and Wigner are reformulated using the notion of direct limit. A definition for contraction of Lie algebra representations based on this reformulation is given. The contractions...

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Published inJournal of physics. Conference series Vol. 343; no. 1; pp. 12116 - 11
Main Authors Subag, E M, Baruch, E M, Birman, J L, Mann, A
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2012
Subjects
Algebra
Lie groups
Physics
Representations
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Summary:In this paper the frequently used procedures for contraction of Lie algebra representations which were introduced by Inönü and Wigner are reformulated using the notion of direct limit. A definition for contraction of Lie algebra representations based on this reformulation is given. The contractions of the skew-Hermitian irreducible representations of so(3) to those of iso(2) and of iso(1,1) to those of Heisenberg Lie algebra are given as examples.
Bibliography:ObjectType-Article-1
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/343/1/012116