相关论文: Universal T-matrix for Twisted Quantum gl(N)

The standard Faddeev quantization of the simple groups is modified in such a way that the quantum analogs of the nonsemisimple groups are obtained by contractions. The contracted quantum groups are regarded as the algebras of noncommutative…

In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal…

In this short article, we obtained some equivalent formulations of property $T$ for a general locally compact quantum group $\mathbb{G}$, in terms of the full quantum group $C^*$-algebras $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ and the…

Here we consider two algebras, a free unital associative complex algebra (denoted by ${\mathcal{B}}$) equiped with a multiparametric \textbf{\emph{q}}-differential structure and a twisted group algebra (denoted by ${\mathcal{A}(S_{n})}$),…

In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…

A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit. For the transformed matrix, the…

Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra and let $U_q(\mathfrak{g})$ denote the corresponding quantized enveloping algebra. In the present paper we show that quantum symmetric pair coideal subalgebras $B_{c,s}$ of…

We first examine how T-matrix equivalence drives the flow of similarity renormalization group (SRG) evolved potential matrix elements to a universal form, with the ultimate goal of gaining insight into universality for three-nucleon forces.…

We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra $H$ endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection equation, yielding an action of cylindrical braid groups…

Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this…

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…

We study the discrete groups $\Lambda$ whose duals embed into a given compact quantum group, $\hat{\Lambda}\subset G$. In the matrix case $G\subset U_n^+$ the embedding condition is equivalent to having a quotient map $\Gamma_U\to\Lambda$,…

We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…

It is known that any covering space of a topological group has the natural structure of a topological group. This article discusses a noncommutative generalization of this fact. A noncommutative generalization of the topological group is a…

On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat…

Let $R$ be a finite commutative ring with identity and $U(R)$ be its group of units. In 2005, El-Kassar and Chehade presented a ring structure for $U(R)$ and as a consequence they generalized this group of units to the generalized group of…

We introduce and study a class of two-dimensional integrable quantum field theories that carry an internal $\mathbb{Z}_n$ structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual…

We discuss quantum dynamical elliptic R-matrices related to arbitrary complex simple Lie group G. They generalize the known vertex and dynamical R-matrices and play an intermediate role between these two types. The R-matrices are defined by…

Let g be a complex, simple Lie algebra and t a Cartan subalgebra of g. A new unitary, flat connection on t with values in any finite-dimensional g-module V and simple poles along the root hyperplanes was recently introduced by J. Millson…