2018/02/05 by Basile Herlemont, Herlemont, Basile
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1802.01357
openalex publication_date 2018/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ring Diffh(n) of h-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the h-deformed vector spaces of \mathfrakgl-type. In contrast to the q-deformed vector spaces for which 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. We show that the center of Diffh,σ(n) is a ring of polynomials in n variables. We construct an isomorphism between certain localizations of Diffh,σ(n) and the Weyl algebra Wn extended by n indeterminates. We present some conditions for the irreducibility of the finite dimensional Diffh,σ(n)-modules. Finally, we discuss difficulties for finding analogous constructions for the ring Diffh(n,N) formed by several copies of Diffh(n).