2003/04/28 by Marcelo Laca, Sergey Neshveyev, Laca, Marcelo +1 · 1 citation
Mathematics · Physics and Astronomy · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0304435
arxiv created 2003/04/28 · openalex publication_date 2003/04/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A continuous one-parameter group of unitary isometries of a right Hilbert C*-bimodule induces a quasi-free dynamics on the Cuntz-Pimsner C*-algebra of the bimodule and on its Toeplitz extension. The restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial, and the corresponding KMS states of the Toeplitz-Cuntz-Pimsner and Cuntz-Pimsner C*-algebras are characterized in terms of traces on the algebra of coefficients. This generalizes and sheds light onto various earlier results about KMS states of the gauge actions on Cuntz algebras, Cuntz-Krieger algebras, and crossed products by endomorphisms. We also obtain a more general characterization, in terms of KMS weights, for the case in which the inducing isometries are not unitary, and accordingly, the restriction of the quasi-free dynamics to the algebra of coefficients is nontrivial.