This book is largely devoted to the most elementary algebras and \(C^*\)-algebras, namely those which are direct limits of complex semisimple algebras.

Readership

Table of Contents

• Notations
• Nonintegral dimensions and indices in analysis and geometry
• Locally semisimple algebras and their Bratteli diagrams
• The characterization of the dimension groups
• Affine representations of simple dimension groups
• Finite difference equations and continued fractions
• Stationary systems, algebraic number theory, and Williams' problem
• Scales and dimensions for locally semisimple algebras
• The \(K_0\) theory of \(C^*\)-algebras
• An application of the Bott Periodicity Theorem
• Further developments and problems
• References
• Index