Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups

We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain non-commutaive rings of quotients coming from complex powers of quantum group generators; this is applied to explicit calculation of singular vectors in Verma modules over U_{q}(\gtsl_{n+1}). We finally give a definition of a $q-$connection with coefficients in a ring of skew polynomials and study the structure of quantum group modules twisted by a $q-$connection.Comment: 25 page

Analytic Expressions for Singular Vectors of the N=2N=2 Superconformal Algebra

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.Comment: 35 pages, LATE

Singular vectors by Fusions in affine su(2)

Explicit expressions for the singular vectors in the highest weight representations of $A_1^{(1)}$ are obtained using the fusion formalism of conformal field theory.Comment: 7 page

Modification of Structure and Strength Properties of Permanent Joints Under Laser Beam Welding with Application of Nanopowder Modifiers

In the paper we present the results of experimental study of specially prepared nanosize metal-ceramic compositions impact upon structure, microhardness and mechanical properties of permanent joints produced by laser-beam welding of steel and titanium alloy plates

Magnetic force microscopy of epitaxial Fe2CoAl and Co2FeAl Heusler alloy films and microstructures

Research supported by RFBR grant 17-57-45024 IND-a

Fusion and singular vectors in A1{(1)} highest weight cyclic modules

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page