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

Abstract

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.

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