Differential calculus on a novel cross-product quantum algebra

Details Differential calculus on a novel cross-product quantum algebra Differential calculus on a novel cross-product quantum algebra

2003-05-13

arxiv.org/abs/math/0305188v1

Mathematics

Quantum Algebra

4 Pages, Talk given at GROUP24, Paris, July 15-20,2002; to appear in the Proceedings (IoP Conference Series 173)

Scientific paper

We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of quantum groups. Following the R-matrix framework, we construct the L+/- functionals and address the problem of duality for this quantum group. This naturally leads to the construction of a bicovariant differential calculus that depends only on one deformation parameter, respects the cross-product structure and has interesting applications. The corresponding Jordanian and hybrid deformation is also explored.

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