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Jonathan Brown, Lisa Orloff Clark (2014)
Fundamenta Mathematicae
We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is effective, then G is topologically principal.
Kamran, Niky, Robart, Thierry (2001)
Journal of Lie Theory
Buneci, Mădălina Roxana (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
Kirill Mackenzie (2000)
Banach Center Publications
Baianu, Ion C., Glazebrook, James F., Brown, Ronald (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Hamid-Reza Fanaï, Atefeh Hasan-Zadeh (2019)
Mathematica Bohemica
We study a problem of isometric compact 2-step nilmanifolds using some information on their geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric and is a cocompact discrete subgroup of isometries of . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable factorization...
Janusz Grabowski (2016)
Commentationes Mathematicae Universitatis Carolinae
We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.
Larissa V. Sbitneva (2000)
Commentationes Mathematicae Universitatis Carolinae
The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99].
Piotr Stachura (2000)
Banach Center Publications
Jan Kubarski (1995)
Publications du Département de mathématiques (Lyon)
Paterson, Alan L.T. (2000)
Homology, Homotopy and Applications
Bertrand Monthubert (2007)
Banach Center Publications
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
L.A.B. San Martin, O.G. do Rocio (1995)
Semigroup forum
Mackenzie, K.C.H. (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Balcerzak, Bogdan, Kubarski, Jan, Walas, Witold (2002)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
Sbitneva, Larissa V. (2002)
International Journal of Mathematics and Mathematical Sciences
Mucuk, Osman, İçen, İlhan (2001)
International Journal of Mathematics and Mathematical Sciences
Macho-Stadler, M. (2000)
Zapiski Nauchnykh Seminarov POMI
Ronald Brown, Osman Mucuk (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Piotr Stachura (2005)
Fundamenta Mathematicae
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
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