Fixed-points in the cone of traces on a C*-algebra

TY - JOUR

T1 - Fixed-points in the cone of traces on a C*-algebra

AU - Rørdam, Mikael

PY - 2019

Y1 - 2019

N2 - Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a nonzero fixed-point when acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod’s results say about the existence of invariant traces on (typically nonunital) C*-algebras equipped with an action of a group with the fixed-point property for cones. As an application of these results, we provide results on the existence (and nonexistence) of traces on the (nonuniform) Roe algebra.

AB - Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a nonzero fixed-point when acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod’s results say about the existence of invariant traces on (typically nonunital) C*-algebras equipped with an action of a group with the fixed-point property for cones. As an application of these results, we provide results on the existence (and nonexistence) of traces on the (nonuniform) Roe algebra.

UR - http://www.scopus.com/inward/record.url?scp=85070268517&partnerID=8YFLogxK

U2 - 10.1090/tran/7797

DO - 10.1090/tran/7797

M3 - Journal article

AN - SCOPUS:85070268517

SN - 0002-9947

VL - 371

SP - 8879

EP - 8906

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 12

ER -