Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics

Summary, in English

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.

• Författare: Daniel Gonçalves; Johan Öinert; Danilo Royer
• Avdelning/ar: Matematik LTH; Algebra
• Publiceringsår: 2014
• Språk: Engelska
• Sidor: 201-216
• Publikation/Tidskrift/Serie: Journal of Algebra
• Volym: 420
• Länkar: http://dx.doi.org/10.1016/j.jalgebra.2014.07.027
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Partial skew group ring; Leavitt path algebra; Partial topological dynamics; Simplicity
• Status: Published
• Forskningsgrupp: Algebra; Non-commutative Geometry
• ISBN/ISSN/Övrigt: ISSN: 0021-8693