On the biparametric quantum deformation of GL(2) x GL(1)

Details On the biparametric quantum deformation of GL(2) x GL(1) On the biparametric quantum deformation of GL(2) x GL(1)

2002-01-22

arxiv.org/abs/math/0201210v1

J. Math. Phys. 42 (2001) 5431-5443

Mathematics

Quantum Algebra

16 pages LaTeX, published in JMP

Scientific paper

10.1063/1.1407280

We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit its cross-product structure. We derive explictly the associated dual algebra, i.e., the quantised universal enveloping algebra employing the R-matrix procedure. This facilitates construction of a bicovariant differential calculus which is also shown to have a cross-product structure. Finally, a Jordanian analogue of the deformation is presented as a cross-product algebra.

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