Differential Calculus on h-Deformed Spaces

Abstract

We construct the rings of generalized differential operators on the $\mathbf{h}$-deformed vector space of $\mathbf{gl}$-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 $\mathbf{h}$-deformed differential operators ${\mathrm{Diff}}_{\mathbf{h},\sigma }(n)$ is labeled by a rational function $\sigma$ 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 ${\mathrm{Diff}}_{\mathbf{h},\sigma }(n)$.

References in corpus (2)

• Structure constants of diagonal reduction algebras of gl type
• Diagonal reduction algebra and reflection equation

Cited by in corpus (1)

• Symplectic Differential Reduction Algebras and Generalized Weyl Algebras