Entropy of Cuntz’s canonical endomorphism

Marie Choda

Vol. 190 (1999), No. 2, 235–245

DOI: 10.2140/pjm.1999.190.235

Abstract

Let {S_i}_i=1ⁿ be generators of the Cuntz algebra 𝒪_n and let Φ be the *-endomorphism of 𝒪_n defined by Φ(x) = ∑ _i=1ⁿS_ixS_i^∗. Then both of Connes–Narnhofer–Thirring’s entropy h_ϕ(Φ) and Voiculescu’s topological entropy ht(Φ) are log n, where ϕ is the unique log n-KMS state of 𝒪_n. Also Longo’s canonical endomorphism for N ⊂ M have the same entropy log n, where the inclusion N ⊂ M comes from 𝒪_n .

Milestones

Received: 1 July 1997

Revised: 2 October 1998

Published: 1 October 1999