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

Abstract

The q-deformed traces and orbits for the two parametric quantum groups $G{L}_{qp}(2)$ and $G{L}_{qp}(1|1)$ 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 $G{L}_{qp}(2)$ and $G{L}_{qp}(1|1)$. The $G{L}_{qp}(2)$ 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 $G{L}_{qp}(1|1)$, the corresponding covariant algebras contain $N=2$ supersymmetric quantum mechanical subalgebras.

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