Lıe örtü grupoidleri
Lie covering groupoids
- Tez No: 177015
- Danışmanlar: DOÇ.DR. İLHAN İÇEN
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Groupoid, Lie groupoid, covering groupoid, Lie group-groupoid, Lie ring-groupoid
- Yıl: 2007
- Dil: Türkçe
- Üniversite: İnönü Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
Özet yok.
Özet (Çeviri)
If M is a differentiable connected manifold then there exists an universal covering manifold M having unique differentiable structure such that the covering map p : M -> M is differentiable. This fact is also true for connected Lie groups By using this fact, it is proved that the category LGdCov(G) of coverings of connected Lie groupoids which is a generalization of connected Lie groups, and the category LGdOp(G) of actions on some M differentiable manifold are equivalent. Secondly, by introducing Lie group-groupoids the category LGGdCov(G) of coverings of some G Lie group-groupoid and the category LGGdOp(G) of actions of G on connected Lie group M are established. Further, it is shown that these categories are equivalent. Finally, it is presented by launching the notion Lie ring-groupoids, a generalization of Lie group-groupoids, that the category LRGdCov(R) of coverings of R Lie ring-groupoids and the category LRGdOp(R) of actions of R on connected Lie ring M are equivalent.
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