The Inner Structure of Boundary Quotients of Right LCM Semigroups

被引：4

作者：

Aiello, Valeriano ^{[1
]}

Conti, Roberto ^{[2
]}

Rossi, Stefano ^{[3
]}

Stammeier, Nicolai ^{[4
]}

机构：

[1] Univ Geneva, Sect Math, 2-4 Rue Lievre,Case Postale 64, CH-1211 Geneva, Switzerland

[2] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[3] Univ Aldo Moro Bari, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

[4] Univ Oslo, Dept Math, POB 1053, NO-0316 Oslo, Norway

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2020年 / 69卷 / 05期

关键词：

C-ASTERISK-ALGEBRAS; K-THEORY; CARTAN SUBALGEBRAS; WEYL GROUP;

D O I：

10.1512/iumj.2020.69.8006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study distinguished subalgebras and automorphisms of boundary quotients arising from algebraic dynamical systems (G, P, theta). Our work includes a complete solution to the problem of extending Bogolubov automorphisms from the Cuntz algebra in 2 <= p <= infinity generators to the p-adic ring C*-algebra. For the case where P is abelian and C* (G) is a maximal abelian subalgebra, we establish a picture for the automorphisms of the boundary quotient that fix C* (G) pointwise. This allows us to show that they form a maximal abelian subgroup of the entire automorphism group. The picture also leads to the surprising outcome that, for integral dynamics, every automorphism that fixes one of the natural Cuntz subalgebras pointwise is necessarily a gauge automorphism. Many of the automorphisms we consider are shown to be outer.

引用

页码：1627 / 1661

页数：35