Related papers: Fuzzy spaces from tensor models, cyclicity conditi…
By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a…
Rank-three tensor model may be regarded as theory of dynamical fuzzy spaces, because a fuzzy space is defined by a three-index coefficient of the product between functions on it, f_a*f_b=C_ab^cf_c. In this paper, this previous proposal is…
Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a…
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…
Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be…
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 derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
A dynamical fuzzy space might be described in terms of a dynamical three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c of the functions f_a on a fuzzy space. A fuzzy analogue of the general…
The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial…
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…
Given a nonempty set $X$ and a function $f:X \rightarrow X$, three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner…
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 sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
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…
Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator,…
A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.
The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for…
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…