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arXiv · 1704.05330

Differential Calculus on h-Deformed Spaces

Basile Herlemont·Oleg Ogievetsky
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Abstract

We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-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 ${\bf h}$-deformed differential operators $\operatorname{Diff}_{{\bf h},\sigma}(n)$ 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 $\operatorname{Diff}_{{\bf h},\sigma}(n)$.

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BibTeXRIS

Basile Herlemont, Oleg Ogievetsky. 2017-04-18. Differential Calculus on h-Deformed Spaces. https://doi.org/10.3842/sigma.2017.082

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