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q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

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arxiv math/0203201 v1 pith:B6W5AFBJ submitted 2002-03-19 math.QA gr-qchep-thmath-phmath.MPmath.RT

A.M. Gavrilik , A.U. Klimyk (BITP , Kiev) This is my paper · ORCID
classification math.QAgr-qchep-thmath-phmath.MPmath.RT
keywords algebrasrepresentationsorthogonalpseudo-orthogonalq-deformedaccordingactingcartan
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Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting according to Gel'fand--Tsetlin-type formulas. Unitary representations of the q-deformed algebras U_q(so_{n,1}) are found.

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  1. The quantum spin Brauer category

    math.QA 2025-04 accept novelty 7.0 of 10

    The quantum spin Brauer category is a braided diagrammatic category whose Karoubi completion covers all finite-dimensional U_q(so(N)) and U_q(o(N)) modules, including spin modules.

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