Nonstandard q-deformation of the universal enveloping algebra U'(\rm so_n)

1999/11/16 by A. U. Klimyk, Klimyk, A. U. · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical and Theoretical Analysis #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/9911114

5 pages, LaTeX

arxiv created 1999/11/16 · openalex publication_date 1999/11/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe properties of the nonstandard q-deformation U'_q(\rm so_n) of the universal enveloping algebra U(\rm so_n) of the Lie algebra \rm so_n which does not coincide with the Drinfeld--Jimbo quantum algebra U_q(\rm so_n). Irreducible representations of this algebras for q a root of unity q^p=1 are given. These representations act on p^N-dimensional linear space (where N is a number of positive roots of the Lie algebra \rm so_n) and are given by r=\rm dim \rm so_n complex parameters.

Cited by

• Classification of irreducible representations of the q-deformed algebra U'_q(so_n)

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