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- W2992045629 abstract "In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie groups. If the groupoid is locally trivial, i.e. a gauge groupoid, the vertical bisections coincide with the gauge group of the underlying bundle. Hence the construction recovers the well known Lie group structure of the gauge groups. To establish the Lie theoretic properties of the vertical bisections of a Lie groupoid over a non-compact base, we need to generalise the Lie theoretic treatment of Lie groups of bisections for Lie groupoids over non-compact bases." @default.
- W2992045629 created "2019-12-13" @default.
- W2992045629 creator A5055081705 @default.
- W2992045629 date "2020-03-01" @default.
- W2992045629 modified "2023-10-16" @default.
- W2992045629 title "The Lie group of vertical bisections of a regular Lie groupoid" @default.
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- W2992045629 doi "https://doi.org/10.1515/forum-2019-0128" @default.
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