On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization

We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ 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 $r$-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of $\mathfrak{g}$. We give complete classification of quasi-trigonometric $r$-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 $\mathfrak{sl}(n)$.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 $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl} (2;\mathbb{C})$. 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 $\mathfrak{o}(3,1)$ as the D=3 de-Sitter algebra and calculate the contraction limit $R\to\infty$ ($R$ -- 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 $\kappa$-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 Uq[gl(n/m)]U_q[gl(n/m)] and related q-identities

Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ 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 $q$-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..