Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics
Gonçalves, Daniel; Öinert, Johan; Royer, Danilo (2014). Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics. Journal of Algebra, 420,, 201 - 216
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Published
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English
Authors:
Gonçalves, Daniel
;
Öinert, Johan
;
Royer, Danilo
Department:
Mathematics (Faculty of Engineering)
Algebra
Non-commutative Geometry-lup-obsolete
Research Group:
Algebra
Non-commutative Geometry-lup-obsolete
Abstract:
Let A be a commutative and associative ring (not necessarily unital), G a group and α a partial action of G on ideals of A, all of which have local units. We show that A is maximal commutative in the partial skew group ring A*G if and only if A has the ideal intersection property in A*G. From this we derive a criterion for simplicity of A*G in terms of maximal commutativity and G-simplicity of A. We also provide two applications of our main results. First, we give a new proof of the simplicity criterion for Leavitt path algebras, as well as a new proof of the Cuntz–Krieger uniqueness theorem. Secondly, we study topological dynamics arising from partial actions on clopen subsets of a compact set.
Keywords:
Partial skew group ring ;
Leavitt path algebra ;
Partial topological dynamics ;
Simplicity
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