17 research outputs found
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
q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1))
For the quantum algebra Uq(gl(n+1)) in its reduction on the subalgebra Uq(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Zq(gl(n+1),gl(n)) is given in terms of the generators and their defining relations. Using this Z-algebra we describe Hermitian irreducible representations of a discrete series for the noncompact quantum algebra Uq(u(n,1)) which is a real form of Uq(gl(n+1)), namely, an orthonormal Gelfand-Graev basis is constructed in an explicit form
Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
We describe in detail two-parameter nonstandard quantum deformation of D=4
Lorentz algebra , linked with Jordanian deformation of
. Using twist quantization technique we obtain
the explicit formulae for the deformed coproducts and antipodes. Further
extending the considered deformation to the D=4 Poincar\'{e} algebra we obtain
a new Hopf-algebraic deformation of four-dimensional relativistic symmetries
with dimensionless deformation parameter. Finally, we interpret
as the D=3 de-Sitter algebra and calculate the contraction
limit ( -- de-Sitter radius) providing explicit Hopf algebra
structure for the quantum deformation of the D=3 Poincar\'{e} algebra (with
masslike deformation parameters), which is the two-parameter light-cone
-deformation of the D=3 Poincar\'{e} symmetry.Comment: 13 pages, no figure
Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
This paper together with the previous one (arXiv:hep-th/0604146) presents the
detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf
algebra in terms of complex and real generators. We describe here in detail two
quantum deformations of the D=4 Lorentz algebra o(3,1) obtained by twisting of
the standard q-deformation U_{q}(o(3,1)). For the first twisted q-deformation
an Abelian twist depending on Cartan generators of o(3,1) is used. The second
example of twisting provides a quantum deformation of Cremmer-Gervais type for
the Lorentz algebra. For completeness we describe also twisting of the Lorentz
algebra by standard Jordanian twist. By twist quantization techniques we obtain
for these deformations new explicit formulae for the deformed coproducts and
antipodes of the o(3,1)-generators.Comment: 17 page
Finite-dimensional representations of the quantum superalgebra and related q-identities
Explicit expressions for the generators of the quantum superalgebra
acting on a class of irreducible representations are given. The
class under consideration consists of all essentially typical representations:
for these a Gel'fand-Zetlin basis is known. The verification of the quantum
superalgebra relations to be satisfied is shown to reduce to a set of
-number identities.Comment: 12 page
Electron linacs in NSC KIPT: R&D and application
A review is given about electron linacs of NSC KIPT and their some applications for research of radiation effects in reactor materials, channeling, plasma-beam interactions, geology (gamma-activation analysis of ore samples), as well as sterilization of single-use medical products, modification of polymers and semiconductors, isotope production for nuclear medicine etc
Peroxide route to the synthesis of ultrafine CeO2-Fe2O3 nanocomposite via successive ionic layer deposition
An ultrafine α-CeO2–α-Fe2O3 nanocomposite was prepared from the ultradispersed nanoparticles of cerium (IV) and iron (III) amorphous hydroxides heat-treated at 600 °С and 900 °С in the air. The initial composites were obtained by the successive ionic layer deposition (SILD) method. According to scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX) and powder X-ray diffraction (PXRD), the cerium/iron ratio in the synthesized nanocomposite is close to 1:2, and the α-CeO2 and α-Fe2O3 nanocrystals are isometrically shaped and have an average size of 4 ± 1 and 7 ± 1 nm (600 °С) and 24 ± 2 and 35 ± 3 nm (900 °С), respectively. Transmission electron microscopy (TEM) and selected area electron diffraction (SAED) have shown that nanocrystals are evenly distributed in the composite volume and are spatially conjugated. The formation mechanisms of both initial amorphous composites of cerium (IV) and iron (III) hydroxides and of α-CeO2 and α-Fe2O3 nanocrystals were established. It was shown that synthesis of the initial hydroxide composite using the SILD method proceeds via the formation of amorphous cerium hydroxo-peroxide (CeO(OOH)2). As a result of the study, a schematic mechanism for the formation of a composite based on ultrafine nanocrystals of cerium (IV) and iron (III) oxides has been proposed
Double of the Yangian and rational R-matrices
Studying the algebraic structure of the double DY (g) of the yangian Y (g) we present the triangular decomposition of DY (g) and a factorization for the canonical pairing of the yangian with its dual inside DY (g). As a consequence we obtain an explicit formula for the universal R-matrix of DY (g) and demonstrate how it works in evaluation representations of Y (sl 2 ). We interprete one-dimensional factor arising in concrete representations of R as bilinear form on highest weight polynomials of irreducible representations of Y (g) and express this form in terms of \Gamma functions. 1 Introduction Yangian Y (g) of a simple Lie algebra g was introduced by V.Drinfeld [D1] as a deformation of universal enveloping algebra U(g[t]) of a current algebra g[t]. The yangians Y (g) and quantum affine algebras U q (g) play the role of dynamical symmetries in quantum field theories [BL] [S]. Tensor products of finite-dimensional representations of yangians produce rational solutions of the Yang-Bax..