Robert S. Doran

P-commutativity of the Banach algebra L1**(G)

Let G be a compact abelian group. It is known that the second conjugate space L1**(G) of the group algebra L1(G) is a noneommutative, nonsemisimple, Banach algebra. It is not known if L1**(G) admits an involution. If it does, we show that it is P-coimnutative, and hence enjoys many of the properties of commutative Banach algebras.

Superstrings, Geometry, Topology, and *-algebras

This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in

Pure states and P-commutative Banach *-algebras

K

Characterizations of C[*]-algebras : the Gelfand-Naimark theorems

-homology and twisted

The Mathematical Legacy of Harish-Chandra

K

Automorphic Forms, Automorphic Representations, and Arithmetic

-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models,

A Generalization of a Theorem of Civin and Yood on Banach *‐Algebras

C^*

Group Representations, Ergodic Theory, and Mathematical Physics

-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of

Hodge Theory, Complex Geometry, and Representation Theory

C^*

Extensions of pure positive functionals on Banach *-algebras

-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.|This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in