Differential Calculus on h-Deformed Spaces

Abstract : We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators Diffh,σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings Diffh,σ(n).
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Basile Herlemont, Oleg Ogievetsky. Differential Calculus on h-Deformed Spaces. Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2017, Special Issue on Recent Advances in Quantum Integrable Systems, 13 (13), pp.082. ⟨10.3842/SIGMA.2017.082⟩. ⟨hal-01696326⟩

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