We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

We consider static U(1) monopole in non-commutative space. Up to the second order in the non-commutativity scale θ, we find no non-trivial corrections to the Dirac solution, the monopole mass remains infinite. We argue the same holds for any arbitrary higher order. Some speculation about the nature of non-commutative spacetime and its relation to the cosmological constant is made. Non-commutati...

We propose a new higher-dimensional mechanism to localize scalar fields as well as fermionic and gauge fields. The underlying theory is a six-dimensional non-commutative field theory where non-commutativity is allowed along two extra infinite spatial dimensions and the four-dimensional brane is provided by a scalar soliton living in the non-commutative space. Making use of the powerful correspo...

The non-commutative geometry is revisited from the perspective of a generalized D p-brane. In particular, we analyze the open bosonic string world-sheet description and show that an effective non-commutative description on a D p-brane corresponds to a re-normalized worldvolume. The world-volume correlators are analyzed to make a note on the non-commutative geometry. It is argued that the U(1) g...

Extending earlier work [7], we examine the deformation of the canonical symplectic structure in a cotangent bundle T ⋆ (Q) by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this short note, we claim this can be done consistently when Q is a Lie group.

We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean version and apply worked out formalism in case od an almost-commutative operator. The presented framework is attempt to reconcile non-commutative geometry supersymmetry.

We construct instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide with the commutative solutions and conjecture that the instanton number in R4 is preserved for general noncommutative deformations. We also study noncommutative...

Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum spaces with commutative coordinate algebras. This observation enables the realization of braiding mappings on commutative algebras. The aim of the article is to...

We treat the events determined by a quantum physical state in a non-commutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Sny-der in 1947 and we calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate ...