A three-parameter deformation of the Weyl-Heisenberg algebra: differential calculus and invariance

Details A three-parameter deformation of the Weyl-Heisenberg algebra: differential calculus and invariance A three-parameter deformation of the Weyl-Heisenberg algebra: differential calculus and invariance

1996-09-09

arxiv.org/abs/q-alg/9609008v1

Mathematics

Quantum Algebra

Contribution to the 5th Colloquium on quantum groups and Integrable systems Prague June 1996, 4 pages, Latex

Scientific paper

10.1023/A:1021483726076

We define a three-parameter deformation of the Weyl-Heisenberg algebra that generalizes the q-oscillator algebra. By a purely algebraical procedure, we set up on this quantum space two differential calculi that are shown to be invariant on the same quantum group, extended to a ten-generator Hopf-star-algebra. We prove that, when the values of the parameters are related, the two differential calculi reduce to one that is invariant under two quantum groups.

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