Kolloquium: W. D. van Suijlekom (Radboud Universiteit): “A Generalization of K-Theory to Operator Systems”

A Generalization of K-Theory to Operator Systems - Vortragender: W. D. van Suijlekom, Radboud Universiteit Nijmegen - Einladender: H. Schulz-Baldes

Abstract:
We propose a generalization of K-theory to operator systems. Motivated by
spectral truncations of noncommutative spaces described by C*-algebras and
inspired by the realization of the K-theory of a C*-algebra as the Witt group
of hermitian forms, we introduce new operator system invariants indexed by the
corresponding matrix size. A direct system is constructed whose direct limit
possesses a semigroup structure, and we define the K0-group as the
corresponding Grothendieck group. This is an invariant of unital operator
systems, and, more generally, an invariant up to Morita equivalence of operator
systems. For C*-algebras it reduces to the usual definition. We illustrate our
invariant by means of the spectral localizer.