相关论文: The coloured quantum plane

The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…

Let (\Gamma,d) be the 3D-calculus or the 4D_{\pm}-calculus on the quantum group SU_q(2). We describe all pairs (\pi, F) of a *-representation \pi of O(SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical…

We quantize punctured plane, $X=\mathbb{R}^2-\{0\}$, employing Isham's group theoretic quantization procedure. After sketching out a brief review of group theoretic quantization procedure, we apply the quantization scheme to the phase…

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…

We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit…

The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement. We review several aspects…

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible…

The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…

A standard bicovariant differential calculus on a quantum matrix space ${\tt Mat}(m,n)_q$ is considered. The principal result of this work is in observing that the $U_q\frak{s}(\frak{gl}_m\times \frak{gl}_n))_q$ is in fact a…

We construct an injective algebra homomorphism of the quantum group $U_q(\mathfrak{sl}_{n+1})$ into a quantum cluster algebra $\mathbf{L}_n$ associated to the moduli space of framed $PGL_{n+1}$-local systems on a marked punctured disk. We…

For G a group, we present a G-graded version of chromatic maps and skein modules and use them to define a 2+1-G-HQFT out of a G-chromatic category. The construction applies to the representations of unrestricted quantum groups at root of…

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…

Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin's construction can be extended for quantum spaces which are non-quadratic homogeneous algebras.…

The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…

As a contribution of the programme of Goswami and Mandal (2014), we carry out explicit computations of $\mathbb{Q}(\Gamma,S)$, the quantum isometry group of the canonical spectral triple on $C_{r}^{*}(\Gamma)$ coming from the word length…

In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with…

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…