A tracial characterization of Furstenberg's xp, xq conjecture

被引：0

作者：

Bruce, Chris ^{[1
]}

Scarparo, Eduardo ^{[2
]}

机构：

[1] Univ Glasgow, Sch Math & Stat, Univ Pl, Glasgow G128QQ, Scotland

[2] Univ Fed Pelotas, Ctr Engn, Pelotas, Brazil

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2024年 / 67卷 / 01期

关键词：

Furstenberg conjecture; tracial states; primitive ideals; K-theory; C-ASTERISK-ALGEBRAS; MULTI-INVARIANT SETS; STATES;

D O I：

10.4153/S0008439523000693

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers p and q, we show that Furstenberg's xp, xq conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the C*-algebra of the group Z[1/pq] (sic) Z(2). We also compute the primitive ideal space and K-theory of C*( Z[1/pq] (sic) Z(2)).

引用

页码：244 / 256

页数：13

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