KMS states on Nica-Toeplitz algebras of product systems

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Abstract

We investigate KMS states of Fowler's Nica-Toeplitz algebra NT(X) associated to
a compactly aligned product system X over a semigroup P of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product system of finite type is introduced. If (G, P) is a lattice ordered group and X is a product system of finite type over P satisfying certain coherence properties, we construct KMS_beta states of NT(X) associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our results were motivated by, and generalize some of the results
of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers.
Original languageEnglish
JournalInternational Journal of Mathematics
Volume23
Issue number12
Pages (from-to)1250123
Number of pages38
ISSN0129-167X
DOIs
Publication statusPublished - Dec 2012

Keywords

  • C*-algebra
  • KMS state
  • product system
  • Hilbert bimodule

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