This article is cited in 3 papers

Rings of $\mathbf h$-deformed differential operators

O. V. Ogievetskii^ab, B. Herlemont<sup>b

a</sup> Kazan Federal University, Kazan, Russia
^b Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

Abstract: We describe the center of the ring $\operatorname{Diff}_{\mathbf{h}}(n)$ $\mathbf{h}$-deformed differential operators of type A. We establish an isomorphism between certain localizations of $\operatorname{Diff}_{\mathbf{h}}(n)$ and the Weyl algebra $\mathrm{W}_n$, extended by $n$ indeterminates.

Keywords: reduction algebra, oscillatory realization, ring of differential operators, Gelfand–Kirillov conjecture, dynamical Yang–Baxter equation.

Received: 24.12.2016
Revised: 22.02.2017

DOI: 10.4213/tmf9328

 English version: Theoretical and Mathematical Physics, 2017, 192:2, 1218–1229

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