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\(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations. (English) Zbl 0735.17020
Summary: 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 \(U_ q(\text{so}_{n,1})\) are found.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E43 Structure and representation of the Lorentz group
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