Journal of Operator Theory
Volume 83, Issue 1, Winter 2020 pp. 73-93.
Phase transitions on
$C^*$-algebras arising from number fields and the generalized Furstenberg conjecture
Authors:
Marcelo Laca (1), Jacqueline M. Warren (2)
Author institution:(1) Department of Mathematics and Statistics,
University of Victoria, Canada
(2) Department of Mathematics, University of
California, San Diego, U.S.A.
Summary: We describe the low-temperature extremal KMS states of the semigroup
$C^*$-algebra of the $ax+b$ semigroup of algebraic integers in a number field
in terms of ergodic invariant measures for certain groups of linear toral
automorphisms. We classify different behaviours in terms of the ideal class
group, the degree, and the unit rank of the field and we also obtain an
explicit description of the primitive ideal space of
the associated transformation group $C^*$-algebra for number fields of unit rank
at least 2 that are not complex multiplication fields.
DOI: http://dx.doi.org/10.7900/jot.2018jul13.2201
Keywords: KMS state, phase transition, $ax+b$ semigroup $C^*$-algebra, primitive ideal
Contents
Full-Text PDF