Related papers: R-matrix and inverse Shapovalov form
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…
In this paper, we construct quantum invariants for knotoid diagrams in $\mathbb{R}^2$. The diagrams are arranged with respect to a given direction in the plane ({\it Morse knotoids}). A Morse knotoid diagram can be decomposed into basic…
In this study, approximate solution of Kuramoto-Sivashinsky Equation, by the reduced differential transform method, are presented. We apply this method to an example. Thus, we have obtained numerical solution Kuramoto-Sivashinsky equation.…
In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions naturally appear in this setting. As an application, we use a…
Twisted tensor powers of quasitriangular Hopf algebras with diagonal sub-Hopf-algebras (self-diagonal tensor powers) are introduced together with their duals and their mutual *-structures as generalizations of the Drinfel'd double as given…
We show that when a torus $T$ acts on a smooth variety $X$, the twisted HKR isomorphism is equivariant. The main consequence is that the Bezrukavnikov- Lachowska isomorphism, relating the Hochschild cohomology of the principal block of the…
In this paper will be considered standard forms of generalized inverses for matrices in the shape of block representations {1, 2, 3, 4, 5, 5^k}-inverse. Especially will be considered Moore-Penrose inverse and the group inverse. Results from…
R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
We give an explicit formula for invariant *-products on a wide class of coadjoint orbits. The answer is expressed in terms of the Shapovalov pairing for generalized Verma modules.
Let $U_\hbar\mathfrak{g}$ denote the Drinfeld-Jimbo quantum group associated to a complex semisimple Lie algebra $\mathfrak{g}$. We apply a modification of the $R$-matrix construction for quantum groups to the evaluation of the universal…
Anna Melnikov provided a parametrization of Borel orbits in the affine variety of square-zero $n \times n$ matrices by the set of involutions in the symmetric group. A related combinatorics leads to a construction a Bott-Samelson type…
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie superalgebra $osp(1|2)$. The twist element is the same as for the $sl(2)$ Lie algebra due to the embedding of the $sl(2)$ into the superalgebra $osp(1|2)$. The…
An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to the generalized Lagrange and the Kowalevski tops. The…
We present further examples of the correspondence between solutions of type IIB supergravity and classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). In the previous works, classical $r$-matrices have been composed…
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
Let $H$ be the quantum double of a Nichols algebra of diagonal type. We compute the $R$-matrix of 3-uples of modules for general finite-dimensional highest weight modules over $H$. We calculate also a multiplicative formula for the…
We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…
By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK…