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.
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Year 2018,
Volume: 47 Issue: 4, 845 - 854, 01.08.2018
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. Ştiint. 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.
Gürsoy, M. H., & İçen, İ. (2018). Coverings of structured Lie groupoids. Hacettepe Journal of Mathematics and Statistics, 47(4), 845-854.
AMA
Gürsoy MH, İçen İ. Coverings of structured Lie groupoids. Hacettepe Journal of Mathematics and Statistics. August 2018;47(4):845-854.
Chicago
Gürsoy, M. Habil, and İlhan İçen. “Coverings of Structured Lie Groupoids”. Hacettepe Journal of Mathematics and Statistics 47, no. 4 (August 2018): 845-54.
EndNote
Gürsoy MH, İçen İ (August 1, 2018) Coverings of structured Lie groupoids. Hacettepe Journal of Mathematics and Statistics 47 4 845–854.
IEEE
M. H. Gürsoy and İ. İçen, “Coverings of structured Lie groupoids”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 4, pp. 845–854, 2018.
ISNAD
Gürsoy, M. Habil - İçen, İlhan. “Coverings of Structured Lie Groupoids”. Hacettepe Journal of Mathematics and Statistics 47/4 (August 2018), 845-854.
JAMA
Gürsoy MH, İçen İ. Coverings of structured Lie groupoids. Hacettepe Journal of Mathematics and Statistics. 2018;47:845–854.
MLA
Gürsoy, M. Habil and İlhan İçen. “Coverings of Structured Lie Groupoids”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 4, 2018, pp. 845-54.
Vancouver
Gürsoy MH, İçen İ. Coverings of structured Lie groupoids. Hacettepe Journal of Mathematics and Statistics. 2018;47(4):845-54.