Classification and Realizations of Type III Factor Representations of Cuntz–Krieger Algebras Associated with Quasi-Free States

2008/06/30 by Katsunori Kawamura
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA #msc:46K10 #msc:46L30

paper · pdf · doi:10.1007/s11005-009-0304-9

11 pages

openalex publication_date 2009/02/18 · arxiv created 2009/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We completely classify type III factor representations of Cuntz-Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type \rm II₁ factor representations are used in these realizations.

Citations

• A class ofC *-algebras and topological Markov chains