Associativity of crossed products by partial actions, enveloping actions and partial representations

Authors:
M. Dokuchaev and R. Exel

Journal:
Trans. Amer. Math. Soc. **357** (2005), 1931-1952

MSC (2000):
Primary 16S99; Secondary 16S10, 16S34, 16S35, 16W22, 16W50, 20C07, 20L05

Published electronically:
July 22, 2004

MathSciNet review:
2115083

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a partial action of a group on an associative algebra , we consider the crossed product . Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of obtained in the context of -algebras. In particular, we prove that is associative, provided that is semiprime. We also give a criterion for the existence of a global extension of a given partial action on an algebra, and use crossed products to study relations between partial actions of groups on algebras and partial representations. As an application we endow partial group algebras with a crossed product structure.

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Additional Information

**M. Dokuchaev**

Affiliation:
Departamento de Matemática, Universidade de São Paulo, Brazil

Email:
dokucha@ime.usp.br

**R. Exel**

Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Brazil

Email:
exel@mtm.ufsc.br

DOI:
https://doi.org/10.1090/S0002-9947-04-03519-6

Keywords:
Partial action,
crossed product,
partial representation,
partial group ring,
grading,
groupoid

Received by editor(s):
February 19, 2003

Received by editor(s) in revised form:
September 26, 2003

Published electronically:
July 22, 2004

Additional Notes:
This work was partially supported by CNPq of Brazil (Proc. 301115/95-8, Proc. 303968/85-0)

Article copyright:
© Copyright 2004
M. Dokuchaev and R. Exel