Restriction and extension of partial actions

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Bagio, Dirceu¹  Paques, Antonio²  Pinedo, Hector³ 

[1] Univ Fed Santa Maria, Dept Matemat, BR-97105900 Santa Maria, RS, Brazil

[2] Univ Fed Porto Alegre, Inst Matemat & Estat, BR-91509900 Porto Alegre, RS, Brazil

[3] Univ Ind Santander, Escuela Matemat, Cm 27 Calle 9 UIS Edificio 45, Bucaramanga, Colombia

关键词: Partial action;    Groupoid;    Extension;    Restriction;    Globalization;    Morita theory;    Galois theory;   

DOI  :  10.1016/j.jpaa.2020.106391

来源: Elsevier

【 摘 要 】

Given a partial action alpha = (A(g), alpha g)(g is an element of G) of a connected groupoid G on a ring A and an object x of G, the isotropy group G(x) acts partially on the ideal A(x) of A by the restriction of alpha. In this paper we investigate the following reverse question: under which conditions a partial group action of G(x) on an ideal of A can be extended to a partial groupoid action of G on A? The globalization problem and some applications to the Morita and Galois theories are also considered. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free