Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897281 | Journal of Pure and Applied Algebra | 2018 | 22 Pages |
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 Câ-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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Roozbeh Hazrat, Huanhuan Li,