nLab
commutative C-star-algebra

Contents

Context

Algebra

Operator algebra

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

A commutative C *C^\ast-algebra is a C-star algebra whose underlying associative algebra is a commutative algebra.

Properties

Relation to topological spaces

Commutative C *C^\ast-algebras are those identified by Gelfand duality with algebras of continuous functions on compact Hausdorff topological spaces.

Relation to KK-theory

Example

Every commutative C-algebra is a nuclear C*-algebra.

(…)

Last revised on July 23, 2018 at 06:28:44. See the history of this page for a list of all contributions to it.