The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that Inn(A) Inn0(A) is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, Inn(A) Inn0(A) is totally disconnected. Another consequence of our results is the following: Suppose A is the tran...

Extended BRST invariance (BRST plus anti-BRST invariances) provides in principle a natural way of introducing the complete gauge fixing structure associated to a gauge field theory in the minimum representation of the algebra. However, as it happens in topological Yang Mills theory, not all gauge fixings can be obtained from a symmetrical extended BRST algebra, where antighosts belong to the sa...

Our aim is to establish the Lebesgue decomposition for strongly-bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly-bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly-bounded additive functions defined on an algeb...

We describe a new first-order formulation of D = 11 supergravity which shows that that theory can be understood to arise from a certain topological field theory by the imposition of a set of local constraints on the fields, plus a lagrange multiplier term. The topological field theory is of interest as the algebra of its constraints realizes the D = 11 supersymmetry algebra with central charges...

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 ...

The language of while programs is a fundamental model for imperative programming on any data type. It leads to a generalisation of the theory of computable functions on the natural numbers to the theory of computable functions on any many-sorted algebra. The language is used to express many algorithms in scientiic computing where while programs are applied to continuous data. In the theory of d...

Motivated by the study of periods automorphic forms and relative trace formulae, we develop theory descent necessary to orbital integrals arising in fundamental lemma for a general class symmetric spaces over p-adic field F. More precisely, prove that connected space F enjoys notion topological Jordan decomposition, which may be independent interest, establish version Kazhdan played crucial rol...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

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 ...