Graded Steinberg algebras and partial actions

Roozbeh Hazrat, Huanhuan Li

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space which is totally disconnected, the Steinberg algebra of the associated groupoid is graded isomorphic to the corresponding partial skew group ring. We show that there is a one-to-one correspondence between the open invariant subsets of the topological space and the graded ideals of the partial skew group ring. We also consider the algebraic version of the partial C⁎-algebra of an abelian group and realise it as a partial skew group ring via a partial action of the group on a topological space. Applications to the theory of Leavitt path algebras are given.
Original languageEnglish
Pages (from-to)3946-3967
Number of pages22
JournalJournal of Pure and Applied Algebra
Volume222
Issue number12
DOIs
Publication statusPublished - 2018

Keywords

  • algebra
  • isomorphisms (mathematics)

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