Deformed Traces and Covariant Quantum Algebras for Quantum Groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$

Details Deformed Traces and Covariant Quantum Algebras for Quantum Groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$ Deformed Traces and Covariant Quantum Algebras for Quantum Groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$

2003-09-18

arxiv.org/abs/hep-th/0309186v4

Phys.Lett. B280 (1992) 219-226

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 11 pages, a note and a reference added, relevant to hep-th/0309127

Scientific paper

10.1016/0370-2693(92)90058-C

The q-deformed traces and orbits for the two parametric quantum groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$ are defined. They are subsequently used in the construction of $q$-orbit invariants for these groups. General $qp$-(super)oscillator commutation relations are obtained which remain invariant under the coactions of groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$. The $GL_{qp}(2)$ covariant deformed algebra is deduced in terms of the bilinears of bosonic $qp$-oscillators which turns out to be a central extension of the Witten-type deformation of $sl(2)$ algebra. In the case of the supergroup $GL_{qp}(1|1)$, the corresponding covariant algebras contain $N = 2$ supersymmetric quantum mechanical subalgebras.

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