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

På svenska

Author

  • Daniel Gonçalves
  • Johan Öinert
  • Danilo Royer

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.

Publishing year

2014

Language

English

Pages

201-216

Publication/Series

Journal of Algebra

Volume

420

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Partial skew group ring
  • Leavitt path algebra
  • Partial topological dynamics
  • Simplicity

Status

Published

Research group

  • Algebra
  • Non-commutative Geometry

ISBN/ISSN/Other

  • ISSN: 0021-8693