27 citations · 140 across the 21 of their papers we have counts for
5 papers · 1 filter
Double quantization on the coadjoint representation of sl(n)
J. Donin
For $\g=sl(n)$ we construct a two parametric $U_h(\g)$-invariant family of algebras, $(S\g)_{t,h}$, which defines a quantization of the function algebra $S\g$ on the coadjoint repr…
Two types of Poisson pencils and related quantum objects
D. Gurevich, J. Donin, V. Rubstov
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmet…
Quantization of function algebras on semisimple orbits in $\g^*$
Joseph Donin, Dmitry Gurevich, Steven Shnider
In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on…
Deformations of quadratic algebras and the corresponding quantum semigroups
J. Donin, S. Shnider
Let be a finite dimensional vector space. Given a decomposition , define quadratic algebras where . This dec…
Quantization of quadratic Poisson brackets on a polynomial algebra of three variables
J. Donin, L. Makar-Limanov
Poisson brackets (P.b) are the natural initial terms for the deformation quantization of commutative algebras. There is an open problem whether any Poisson bracket on the polynomia…