We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...

Motivated by research on how topology may be a helpful foundation for building information modeling (BIM), a relational database version of the notions of chain complex and chain complex morphism is defined and used for storing cw-complexes and their morphisms, hence instances of building projects and different views upon them, into relational databases. In many cases, this can be done without ...

When Aut(A) and Homeo(Prim(A)) are homeomorphic, where A is a C *-algebra Abstract In this paper, we discuss when Aut(A) and Homeo(Prim(A)) are homeomorphic, where A is a C *-algebra. 1 Preliminaries Let A be C *-algebra. Then the collection Aut(A) of ⋆-automorphisms of A is a group under composition. We give Aut(A) the point-norm topology, that is, α n → α if and only if α n (a) → α(a) for all...

We obtain a new free field realization of N = 2 super W3 algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra sl(3|2)(1) associated with a non-standard sl(2) embedding. After twisting and a similarity transformation, this W algebra can be identified as the extended topological conf...

The field content of the two dimensional string theory consists of the dynamical tachyon field and some nonpropagating fields which consist in the topological sector of this theory. We propose in this paper to study this topological sector as a spacetime gauge theory with a simple centrally extended w∞ algebra. This w∞ algebra appears in both the world sheet BRST analysis and the matrix model a...

Topological quantum field theories containing matter fields are constructed by twisting N = 2 supersymmetric quantum field theories. It is shown that N = 2 chiral (antichiral) multiplets lead to topological sigma models while N = 2 twisted chiral (twisted antichiral) multiplets lead to Landau-Ginzburg type topological quantum field theories. In addition, topological gravity in two dimensions is...

This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the Koopman operator and the existence of a topological conjugacy between the nonlinear dynamics and its linearization in the neighborhood of the fixed point. Th...

Following ideas of A. C. Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.

This is the final one in the series of papers where we introduce and study the C∗-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C∗-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C∗-algebras associated with topological graphs. 0. Introduc...

We show that the BRST structure of the topological string is encoded in the “small” N = 4 superconformal algebra, enabling us to obtain, in a non-trivial way, the string theory from hamiltonian reduction of A(1|1). This leads to the important conclusion that not only ordinary string theories, but topological strings as well, can be obtained, or even defined, by hamiltonian reduction from WZW mo...