Coverings of structured Lie groupoids

Year 2018, Volume: 47 Issue: 4, 845 - 854, 01.08.2018

M. Habil Gürsoy , İlhan İçen

Abstract

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 group-groupoid 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.

Keywords

Lie Groupoid , Covering , Structured Lie Groupoid

References

• Brown, R., Topology and Groupoids, BookSurge LLC, Deganwy, United Kingdom, 2006.
• Brown, R., Danesh-Naruie, G. and Hardy, J.P.L., Topological Groupoids II: Covering mor- phisms and G-spaces, Math. Nachr, 74, 143-145, 1976.
• Brown, R. and Spencer, C. B., G-groupoids, Crossed Modules and the Fundamental Groupoid of a Topological Group, Proc. Konn. Ned. Akad. v. Wet., 79, 196-302, 1976.
• Danesh-Naruie, G., Theory of Topological Groupoids, PhD. Thesis, The University of Southampton, England, 1970.
• Gabriel, P. and Zisman, M., Categories of Fractions and Homotopy Theory, Springer-Verlag, Heidelberg, 1967.
• Gursoy, M.H., Icen, I., Ozcan, A.F., Coverings and Actions of Structured Lie Groupoids, An. Ş“tiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 2, 661-679, 2016.
• Higgins,P.J., Categories and Groupoids, van Nostrand, New York, 1971.
• Icen, I., Gürsoy, M.H., Ozcan, A.F., Coverings of Lie Groupoids, Turk. J. Math., 35, 207- 218, 2011.
• Icen, I., Ozcan, A.F. and Gursoy, M.H., Topological Group-Groupoids and Their Coverings, Indian J. pure appl. Math, 36 (9), 493-502, 2005.
• MacKenzie, K.C.H., General Theory of Lie Groupoids and Lie Algebroids, London Mathe- matical Society Lecture Note Series 213, Cambridge University Press, 2005.
• Moerdijk, I. and Mrcun, J., Introduction to Foliations and Lie Groupoids, Cambridge Uni- versity Press, New York, 2003.
• Mucuk, O., Coverings and Ring-Groupoids, Georgian Math. J., Vol:5, No:5, 475-482, 1998.
• Ozcan, A.F., Icen, I. and Gursoy, M.H., Topological Ring-Groupoids and Liftings, Iranian Journal of Science and Technology, Transaction A, Vol. 30, No.A3, 2006.