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Quantum Lie superalgebras and q-oscillators. (English) Zbl 0764.17023
Summary: Quantum deformation of the simple Lie superalgebras is formulated applying both the method of the Cartan matrix and the \(R\)-matrix approach. Using the quantum analogue of Bose and Fermi oscillators, the realization of quantum \(sl_ q(n| m)\) generators is given. The \(q\)- oscillators are obtained from the quantum algebra itself by the contraction method. Multimode representations in terms of \(q\)-oscillators require nontrivial couplings between the different modes. Possible applications are outlined.

MSC:
17B81 Applications of Lie (super)algebras to physics, etc.
81T60 Supersymmetric field theories in quantum mechanics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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