nLab
operator K-theory

Context

Index theory

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

A variant of algebraic K-theory for operator algebras (Banach algebras and in particular C-star algebras) is operator K-theory: it generalizes topological K-theory via the Serre-Swan theorem from commutative C-star algebras to general C *C^\ast-algebras.

geometric contextuniversal additive bivariant (preserves split exact sequences)universal localizing bivariant (preserves all exact sequences in the middle)universal additive invariantuniversal localizing invariant
noncommutative algebraic geometrynoncommutative motives Mot addMot_{add}noncommutative motives Mot locMot_{loc}algebraic K-theorynon-connective algebraic K-theory
noncommutative topologyKK-theoryE-theoryoperator K-theory

References

A standard textbook account is in section 2 of

Other introductions include

  • M. Rørdam, F. Larsen, N. Laustsen, An introduction to K-theory for C *C^\ast-algebras, London Mathematical Society Student Textx

Revised on December 12, 2016 05:41:35 by Urs Schreiber (131.220.199.167)