Coverings of Lie groupoids

Içen, İlhan; Gürsoy, Mustafa Habil; Özcan, A. Fatih

doi:10.3906/mat-0902-2

Cited by 2 publications

(6 citation statements)

References 6 publications

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“…the third condition is also satised. Smoothness of the action φ is similar to that in the case of Lie groupoids given in [8]. Thus, we obtain a Lie group-groupoid G M whose objects manifold is…”

Section: Now Let Us Check the Action Conditionsmentioning

confidence: 63%

“…For each x ∈ G0, if the restriction G x → G p( x) of p is a dieomorphism, p is called the covering morphism of Lie groupoids. Then Lie groupoid G is also called the covering of the Lie groupoid G [8].…”

Section: Coverings Of Structured Lie Groupoidsmentioning

confidence: 99%

“…Thus, we obtain the smooth action φ : G α × p 0 H0 → H0, (a, x) → a . x = β( a) of G on M = H0 by w = p0 (for more details, see [8]).…”

Section: Proposition Let Pmentioning

confidence: 99%

“…Let G be a Lie groupoid acting on manifold M via a submersion w : M → G0. By this action, we can dene a Lie groupoid denoted by G M which is called the action Lie groupoid [8].…”

Section: 7mentioning

confidence: 99%

“…In 1956, Ehresmann introduced the concepts of topological and Lie groupoid. As a consequence of this, several algebraic papers are written concerning topological and Lie groupoids [2,8].…”

Section: Introductionmentioning

confidence: 99%

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Coverings of Structured Lie Groupoids

Gürsoy¹,

Içen²

2017

HJMS

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In this work, we present some results related to coverings of structured Lie groupoids. Firstly, we obtain a covering Lie group-groupoid and a covering morphism of Lie group-groupoids from a given Lie groupgroupoid by the notion of action. Secondly, we show how the Lie group structure of a Lie group-groupoid is lifted to a covering Lie groupoid. Then, we give similar results for Lie ring-groupoid which is also a structured Lie groupoid.

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Section: Now Let Us Check the Action Conditionsmentioning

confidence: 63%

Section: Coverings Of Structured Lie Groupoidsmentioning

confidence: 99%

“…Thus, we obtain the smooth action φ : G α × p 0 H0 → H0, (a, x) → a . x = β( a) of G on M = H0 by w = p0 (for more details, see [8]).…”

Section: Proposition Let Pmentioning

confidence: 99%

“…Let G be a Lie groupoid acting on manifold M via a submersion w : M → G0. By this action, we can dene a Lie groupoid denoted by G M which is called the action Lie groupoid [8].…”

Section: 7mentioning

confidence: 99%

“…In 1956, Ehresmann introduced the concepts of topological and Lie groupoid. As a consequence of this, several algebraic papers are written concerning topological and Lie groupoids [2,8].…”

Section: Introductionmentioning

confidence: 99%

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Coverings of Structured Lie Groupoids

Gürsoy¹,

Içen²

2017

HJMS

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Actions of R-module groupoids

Özcan,

İçen

2023

Filomat

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Let R be a ring, 1R be the identity of ring R and N be an R-module on R. In this work, we are going to give a new definition that it is called an action of R-module groupoids. First, we are going to give the definition of the action of the R-module groupoids on the R-module N. Then we obtained a new category RMGpdOp(?) of actions of ? on R-modules. We also find that there is a groupoid ? ?? N on N. ? ?? N is called action R-module groupoid. Finally, we prove that the category RMGpdOp(?) of actions of R-module groupoids is equivalent to RMGpdCov(?) of coverings of R-module groupoids.

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Coverings of Lie groupoids

Cited by 2 publications

References 6 publications

Coverings of Structured Lie Groupoids

Coverings of Structured Lie Groupoids

Actions of R-module groupoids

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