相关论文: On the construction of fuzzy spaces and modules ov…
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 present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…
In this paper, we give a classification of the 3-dimensional associative algebras over the complex numbers, including a construction of the moduli space, using versal deformations to determine how the space is glued together.
We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characterizing the noncommutative plane with a * product and depends…
In this paper, We have introduced a new class of sequences of fuzzy numbers defined by using modulus function and generalized weighted mean over the class defined in \cite{OS}. We have proved that this class form a quasilinear complete…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
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…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
The rank-three tensor models, which have a rank-three tensor as their only dynamical variable, may be interpreted as models of dynamical fuzzy spaces. In this interpretation, the generalized Hermiticity condition on the rank-three tensor…
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…
We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N -> infinity limit, where N labels the…
In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and…
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…
Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are many higher dimensional examples, the most known and most studied fuzzy spaces are…
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
In this paper, we set up the bi-module of the algebra ${\cal A}$ on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are…
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…