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KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
Abstract
For an action of an inverse semigroup S on a locally compact Hausdorff space X, we construct an étale groupoid Sltimes XKS, called the KS-groupoid associated with the action. This construction may be viewed as a dynamical analogue of the construction of universal groupoids for inverse semigroups. We provide a dynamical version of Paterson's theorem which states that the full and reduced crossed products (in the sense of Khoshkam and Skandalis) of C0(X) are canonically isomorphic to the full and reduced groupoid C*-algebras of Sltimes XKS, respectively. We further investigate some topological properties, functoriality and universality of KS-groupoids.
Related
BibTeX
@misc{sekiyama2026ksgroupoids,
title = {{KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions}},
author = {Hikaru Sekiyama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06447},
eprint = {2609.06447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06447},
}
RIS
TY - UNPB
TI - KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
AU - Hikaru Sekiyama
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06447
UR - https://arxiv.org/abs/2609.06447
AB - For an action of an inverse semigroup S on a locally compact Hausdorff space X, we construct an étale groupoid Sltimes X^KS, called the KS-groupoid associated with the action. This construction may be viewed as a dynamical analogue of the construction of universal groupoids for inverse semigroups. We provide a dynamical version of Paterson's theorem which states that the full and reduced crossed products (in the sense of Khoshkam and Skandalis) of C_0(X) are canonically isomorphic to the full and reduced groupoid C*-algebras of Sltimes X^KS, respectively. We further investigate some topological properties, functoriality and universality of KS-groupoids.
ER -