Associativity of crossed products by partial actions, enveloping actions and partial representations |
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Authors: | M Dokuchaev R Exel |
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Institution: | Departamento de Matemática, Universidade de São Paulo, Brazil ; Departamento de Matemática, Universidade Federal de Santa Catarina, Brazil |
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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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Keywords: | Partial action crossed product partial representation partial group ring grading groupoid |
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