A GENERALIZATION OF K-THEORY TO OPERATOR SYSTEMS

Speaker(s)

WALTER VAN SUIJLEKOM

Affiliation

Radboud Universiteit, Nijmegen, The Netherlands

Language of the talk

English

Date

Nov. 26, 2025, 5:15 p.m.

Information about the event

IMPAN - Room 405

Title in Polish

A GENERALIZATION OF K-THEORY TO OPERATOR SYSTEMS

Seminar

North Atlantic Noncommutative Geometry Seminar

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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 that we use to define the K_0-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. It reduces to the usual definition for C*-algebras. We will illustrate our invariant by means of the spectral localizer.

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