We show that the complexification (Ã, τ̃) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (Ã, τ̃) of a commutati...

The Topological N=2 Superconformal algebra has 29 different types of singular vectors (in complete Verma modules) distinguished by the relative U(1) charge and the BRST-invariance properties of the vector and of the primary on which it is built. Whereas one of these types only exists at level zero, the remaining 28 types exist for general levels and can be constructed already at level 1. In thi...

Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of B (= tsr(B)) when A has topological stable rank one. We show that tsr(B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with tsr(D) = 1. When G is a finite group and α is an action of G on UHF, we know that a cr...

The theory of topological algebras and the theory of bases in topological vector spaces are both well-established areas of analysis but only recently have papers appeared combining these two concepts. Of course, no new information about an algebra will be provided by a basis unless some relationship is given between the basis and the multiplicative structure of the algebra. For example, orthogo...

Current research on qualitative spatial representation and reasoning usually focuses on one single aspect of space. However, in real world applications, several aspects are often involved together. This paper extends the well-known RCC8 constraint language to deal with both topological and directional information, and then investigates the interaction between the two kinds of information. Given...

In this paper we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X . The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where t...

The general idea of quantization is to find a way to pass from the classical setting to the quantum one. In the classical situation, we have a symplectic manifold (M,ω) standing for the space of “states” of some physical system. The topological data of the manifold is contained in the structure of the function algebra C(M). The smooth structure on M gives rise to a distinguished subalgebra C∞ 0...

For a simple Lie algebra g, we derive a simple algorithm for computing logarithmic derivatives of tau-functions of Drinfeld–Sokolov hierarchy of g-type in terms of g-valued resolvents. We show, for the topological solution to the lowest-weight-gauge Drinfeld–Sokolov hierarchy of g-type, the resolvents evaluated at zero satisfy the topological ODE.

In this paper, we start with the definitions and properties of the fundamental group of a topological space, and then proceed to prove VanKampen’s Theorem, which helps to calculate the fundamental groups of complicated topological spaces from the fundamental groups we know already. We also use the properties of covering space to prove the Fundamental Theorem of Algebra and Brouwer’s Fixed Point...

We investigate C∗-algebras associated with row-finite topological higherrank graphs with no source, which are based on product system C∗-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose C∗-algebras contain Cuntz’s ax + b-semigroup C∗-alge...