Quantum Heisenberg - Weyl algebras

Quantum Heisenberg–Weyl Algebras

All Lie bialgebra structures on the Heisenberg–Weyl algebra [A+, A−] = M are classified and explicitly quantized. The complete list of quantum Heisenberg–Weyl algebras so obtained includes new multiparameter deformations, most of them being of the non-coboundary type. A Hopf algebra deformation of a universal enveloping algebra Ug defines in a unique way a Lie bialgebra structure (g, δ) on g [1...

A Necessary Condition for Weyl-Heisenberg Frames

A Quadratic Deformation of the Heisenberg-Weyl and Quantum Oscillator Enveloping Algebras

A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains null vectors and so is reducible to a finite dimensional representation. The cyclic, nilpotent and unitary representations are discussed. Witten’s deformation ...

Isomorphisms between quantum generalized Weyl algebras

We study isomorphisms between generalized Weyl algebras, giving a complete answer to the quantum case of this problem for R = k[h].

Discrete Weyl–Heisenberg transforms

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