MORITA EQUIVALENCE OF PARTIAL GROUP ACTIONS AND GLOBALIZATION

被引：10

作者：

Abadie, F. ^{[1
]}

Dokuchaev, M. ^{[2
]}

Exel, R. ^{[3
]}

Simon, J. J. ^{[4
]}

机构：

[1] Univ Republica, Fac Ciencias, Ctr Matemat, Igua 4225, Montevideo 11400, Uruguay

[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP, Brazil

[3] Univ Fed Santa Catarina, Dept Matemat, BR-88040900 Florianopolis, SC, Brazil

[4] Univ Murcia, Dept Matemat, E-30071 Murcia, Spain

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 07期

基金：

巴西圣保罗研究基金会;

关键词：

Partial action; skew group ring; Morita equivalence; C*-algebra; SKEW POLYNOMIAL-RINGS; C-ASTERISK-ALGEBRAS; PARTIAL CROSSED-PRODUCTS; TWISTED PARTIAL ACTIONS; ENVELOPING ACTIONS;

D O I：

10.1090/tran/6525

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a large class of partial actions of groups on rings, called regular, which contains all s-unital partial actions as well as all partial actions on C*-algebras. For them the notion of Morita equivalence is introduced, and it is shown that any regular partial action is Morita equivalent to a globalizable one and that the globalization is essentially unique. It is also proved that Morita equivalent s-unital partial actions on rings with orthogonal local units are stably isomorphic. In addition, we show that Morita equivalent s-unital partial actions on commutative rings must be isomorphic, and an analogous result for C*-algebras is also established.

引用

页码：4957 / 4992

页数：36