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Öğe Coverings and actions of structured Lie groupoids(Universitatii Al.I.Cuza din Iasi, 2016) Gursoy, M.H.; Icen, I.; Ozcan, A.F.In this work we deal with coverings and actions of Lie group-groupoids and Lie ring-groupoids being two sorts of the structured Lie groupoids. After we give definition of a structured Lie groupoid, we prove some characterizations of structured Lie groupoids. Then, we present the concept of covering of a structured Lie groupoid. As first main result of this work, we show that the category LSCov(M) of the smooth coverings of Lie group M is equivalent to the category SLGCov(π1M) of the coverings of structured Lie groupoid π1M, where it is assumed that π1M is a Lie group-groupoid, specially. Furthermore, we define an action of a structured Lie groupoid on a connected Lie structure. Finally, we show that the category SLGCov(G) of the coverings of a structured Lie groupoid G and the category SLGOp(G) of the actions of G on Lie structures (group or ring) are equivalent. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.
