Related papers: Fuzzy Torus via q-Parafermion
We describe a construction of fuzzy spaces which approximate projective toric varieties. The construction uses the canonical embedding of such varieties into a complex projective space: The algebra of fuzzy functions on a toric variety is…
The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine Lie algebra and the second one is a new…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
In this paper, we give some properties of fuzzy Riesz homomorphism on fuzzy Riesz space. We give definitions of fuzzy quotient spaces, and some characterizations of fuzzy Archimedean quotient spaces. We prove the properties which fuzzy…
In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.
We study FTOP(L), a fuzzy category with fuzzy functions in the role of morphisms. This category has the same objects as the category L-TOP of Chang-Goguen L-topological spaces,but an essentially wider class of morphisms - so called fuzzy…
We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a…
In this paper we will prove a series of $q$-identities suggested by the realisation of certain conformal field theories by so-called `coupled free fermions'. We will consider $q$-series arising from coupled free fermions constructed by the…
We construct and discuss the Fock-space representation for a deformed oscillator with "peculiar" statistics. We show that corresponding algebra represents deformed supersymmetric oscillator.
We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.
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…
We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.
A protorus is a compact connected abelian group. We use a result on finite rank torsion-free abelian groups and Pontryagin Duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a…
It is shown that every homeomorphism f of finite distortion in the plane is the so-called lower Q-homeomorphism with Q(z)=K_f(z), and, on this base, it is developed the theory of the boundary behavior of such homeomorphisms.
We study relations between different kinds of non-commutative spheres which have appeared in the context of ADS/CFT correspondences recently, emphasizing the connections between spaces that have manifest quantum group symmetry and spaces…
At the first, we revise the Kosinski definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
We study representations of the non-standard quantum deformation $U'_qso_n$ of $Uso_n$ via a Verma module approach. This is used to recover the classification of finite-dimensional modules for $q$ not a root of unity, given by classical and…