The Nonstandard Deformation U'_q(so_n) For q a Root of Unity

2000/07/17 by N. Z. Iorgov, Iorgov, N. Z., A. U. Klimyk +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical and Theoretical Analysis #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0007105

17 pages, LaTeX

arxiv created 2000/07/17 · openalex publication_date 2000/07/17 · 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(so_n) of the universal enveloping algebra U(so_n) of the Lie algebra so_n which does not coincide with the Drinfeld--Jimbo quantum algebra U_q(so_n). In particular, it is shown that there exists an isomorphism from U'_q(so_n) to U_q(sl_n) and that finite dimensional irreducible representations of U'_q(so_n) separate elements of this algebra. Irreducible representations of the algebras U'_q(so_n) for q a root of unity q^p=1 are given. The main class of these representations act on p^N-dimensional linear space (where N is a number of positive roots of the Lie algebra so_n) and are given by r=dim so_n complex parameters. Some classes of degenerate irreducible representations are also described.

Related

• Nonstandard q-deformation of the universal enveloping algebra U'(\rm so_n)
• Classification of irreducible representations of the q-deformed algebra U'_q(so_n)
• Nonclassical representations of the nonstandard deformations U'_q(so_n), U_q(iso_n) and U'_q(so_n,1)
• Representations of the q-deformed algebra U'_q(so_2,2)
• Representations of Classical Lie Algebras from their Quantum Deformations