期刊
JOURNAL OF PURE AND APPLIED ALGEBRA
卷 222, 期 12, 页码 3946-3967出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jpaa.2018.02.014
关键词
-
资金
- Australian Research Council [DP150101598, DP160101481]
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. (C) 2018 Elsevier B.V. All rights reserved.
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