nLab operator K-theory

Redirected from "algebraic K-theory of operator algebras".

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 $C^\ast$ -algebras.

geometric context	universal additive bivariant (preserves split exact sequences)	universal localizing bivariant (preserves all exact sequences in the middle)	universal additive invariant	universal localizing invariant
noncommutative algebraic geometry	noncommutative motives $Mot_{add}$	noncommutative motives $Mot_{loc}$	algebraic K-theory	non-connective algebraic K-theory
noncommutative topology	KK-theory	E-theory	operator K-theory	…

A standard textbook account is in section 2 of

Other introductions include

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

Last revised on December 12, 2016 at 10:41:35. See the history of this page for a list of all contributions to it.