Quantum Heisenberg--Weyl Algebras

Abstract

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.

8 pages, LaTeX

References in corpus (3)

• Universal $R$-matrix for non-standard quantum $sl(2,\mathbb{R})$
• Lie bialgebra quantizations of the oscillator algebra and their universal $R$--matrices
• A universal non-quasitriangular quantization of the Heisenberg group

Cited by in corpus (7)

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• Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
• Coherent and squeezed states of quantum Heisenberg algebras
• Classification of real three-dimensional Poisson-Lie groups