Related papers: Quantizations of D=3 Lorentz symmetry
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
Nonstandard q-deformed algebras U'_q(so_n), proposed a decade ago for the needs of representation theory, essentially differ from the standard Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with regard to the latter…
We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space…
Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers $\R$. We start with the q-deformed Heisenberg algebra $\cLLq$ which is obtained by the Moyal $\ast$-deformation of the Heisenberg algebra…
An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$…
Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the…
We develop an in-depth analysis of the $SO(4)$ Landau models on $S^3$ in the $SU(2)$ monopole background and their associated matrix geometry. The Schwinger and Dirac gauges for the $SU(2)$ monopole are introduced to provide a concrete…
A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra…
We discuss quantum deformations of Jordanian type for Lie superalgebras. These deformations are described by twisting functions with support from Borel subalgebras and they are multiparameter in the general case. The total twists are…
We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…
Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to…
The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
We say that a formal deformation from an algebra $N$ to algebra $A$ is strongly flat if for every real number $e $ there is a real number $0<s<e$ such that this deformation specialised at $t=s$ gives an algebra isomorphic to $A$. We show…
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…
We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system with a constraint algebra generating the non-compact $SL(2,\mathbb{R})$ group. In particular, we consider three…
If $L$ is a semisimple Lie algebra of vector fields on R^N with a split Cartan subalgebra C, then it is proved that the dimension of the generic orbit of C coincides with the dimension of C. As a consequence one obtains a local canonical…
Beginning with the data of a quiver Q, and its dimension vector d, we construct an algebra D_q=D_q(Mat_d(Q)), which is a flat q-deformation of the algebra of differential operators on the affine space Mat_d(Q). The algebra D_q is…
We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the representations of one of the deformed spacetime…
In this article, matrix and vector formalisms for Lorentz transformations in time ($t$) and two space dimensions ($x$ and $y$) are developed and discussed. Lorentz transformations conserve the squared interval $t^2 - x^2 - y^2$. Examples of…