Related papers: Fuzzy Torus and q-Deformed Lie Algebra
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…
The paper is constructed in two parts.In the first part we introduce the concept of the algebra of Q-meromorphic functions on the quantum plane.The A (q)-algebra of Q-analytic functions considered in[6]is seen as a proper subalgebra. In the…
We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial…
The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study…
The $q$-deformed loop gravity framework was introduced as a canonical formalism for the Turaev-Viro model (with $\Lambda < 0$), allowing to quantize 3D Euclidean gravity with a (negative) cosmological constant using a quantum deformation of…
We investigate mass deformation of twisted superalgebra of U(N) super Yang-Mills (SYM) theories in several models and in several dimensions, motivated by the method formulated in [1]. We show that there are several ways to perform the…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
Let $\Sigma$ be a finite type surface, and $G$ a complex algebraic simple Lie group with Lie algebra $\mathfrak{g}$. The quantum moduli algebra of $(\Sigma,G)$ is a quantization of the ring of functions of $X_G(\Sigma)$, the variety of…
For two $n \times n$ complex matrices $A$ and $B$, we define the $q$-deformed commutator as $[ A, B ]_q := A B - q BA$ for a real parameter $q$. In this paper, we investigate a generalization of the B\"{o}ttcher-Wenzel inequality which…
A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De…
Non-abelian coordinate ring of $U_q(SL(N))$ (quantum deformation of the algebra of functions) for $N=2,3$ is represented in terms of conventional creation and annihilation operators. This allows to construct explicitly representations of…
Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…
In this study, a relativistic formulation of the $(q)$-deformed Dunkl-Fokker-Planck equation in $(1+1)$-dimensions is constructed within the reflection-deformed quantum framework. In this case, the formalism includes $(q)$-deformed Dunkl…
A new trigonometric degeneration of the Sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied. A further contraction gives the standard quantum algebra…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten (WZNW) models at the classical level. The target space is given by squashed S^3 and the isometry is SU(2)_L x U(1)_R. It is known…
In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound…