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

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dc.creatorIorgov, N. Z.
dc.creatorKlimyk, A. U.
dc.date2000-07-17
dc.date.accessioned2026-07-07T04:36:25Z
dc.date.available2026-07-07T04:36:25Z
dc.descriptionWe 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.
dc.description17 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0007105
dc.identifierhttp://arxiv.org/abs/math/0007105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59587
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleThe Nonstandard Deformation U'_q(so_n) For q a Root of Unity
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