an:00009320
Zbl 0735.17020
Gavrilik, A. M.; Klimyk, A. U.
\(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
EN
Lett. Math. Phys. 21, No. 3, 215-220 (1991).
00156762
1991
j
17B37 17B10 22E43
quantum group; q-analogue of Gel'fand-Tsetlin formulas; pseudo-orthogonal deformed algebras; deformed Lorentz algebras
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.