19 research outputs found
New -Matrices for Lie Bialgebra Structures over Polynomials
For a finite dimensional simple complex Lie algebra , Lie
bialgebra structures on and were
classified by Montaner, Stolin and Zelmanov. In our paper, we provide an
explicit algorithm to produce -matrices which correspond to Lie bialgebra
structures over polynomials
On dynamical adjoint functor
We give an explicit formula relating the dynamical adjoint functor and
dynamical twist over nonalbelian base to the invariant pairing on parabolic
Verma modules. As an illustration, we give explicit - and
-invariant star product on projective spaces
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
We study classical twists of Lie bialgebra structures on the polynomial
current algebra , where is a simple complex
finite-dimensional Lie algebra. We focus on the structures induced by the
so-called quasi-trigonometric solutions of the classical Yang-Baxter equation.
It turns out that quasi-trigonometric -matrices fall into classes labelled
by the vertices of the extended Dynkin diagram of . We give
complete classification of quasi-trigonometric -matrices belonging to
multiplicity free simple roots (which have coefficient 1 in the decomposition
of the maximal root). We quantize solutions corresponding to the first root of
.Comment: 41 pages, LATE
Quantum sphere S^4 as a non-Levi conjugacy class
We construct a U_h(sp(4))-equivariant quantization of the four-dimensional
complex sphere S^4 regarded as a conjugacy class, Sp(4)/Sp(2)x Sp(2), of a
simple complex group with non-Levi isotropy subgroup, through an operator
realization of the quantum polynomial algebra C_h[S^4] on a highest weight
module of U_h(sp(4)).Comment: 17 pages, no figure
From dynamical to non-dynamical twists
We provide a construction which gives a twisting element for a universal enveloping algebra starting from a certain dynamical twist. This construction is a quantization of the analogous quasi-classical process given in [Karolinsky and Stolin, Lett. Math. Phys. 60 (2002), 257-274]. In particular, we reduce the computation of the twisting element for the classical r-matrix constructed from the Frobenius algebra the maximal parabolic subalgebra of sl(n) related to the simple root alpha(n-1), to the computation of the universal dynamical twist for sl(n)
Irreducible highest weight modules and equivariant quantization
We consider the relationship between the Shapovalov form on an previous termirreducible highestnext term weight module of a semisimple complex Lie algebra, fusion elements, and equivariant quantization. We also discuss some limiting properties of fusion element
Irreducible highest weight modules and equivariant quantization
We consider the relationship between the Shapovalov form on an previous termirreducible highestnext term weight module of a semisimple complex Lie algebra, fusion elements, and equivariant quantization. We also discuss some limiting properties of fusion element
Equivariant quantization of Poisson homogeneous spaces and Kostant\u27s problem
We find a partial solution to the longstanding problem of Kostant concerning description of the so-called locally finite endomorphisms of highest weight irreducible modules. The solution is obtained by means of its reduction to a far-reaching extension of the quantization problem. While the classical quantization problem consists in finding *product deformations of the commutative algebras of functions, we consider the case when the initial object is already a noncommutative algebra, the algebra of functions within q-calculus