Let (A, M) and p: M|rightarrow M be an arbitrary Lie groupoid and submersion with connected fibers respectively. The aim of the present paper is to define a more general class of differential equations formulated in terms of the theory of groupoids and algebroids. For this purpose the quotient-groupoid (A/p, M) for every Lie groupoid (A, M) and every submersion p is constructed since these equations are defined on Lie algebroids of such groupoids. In particular, it is proved that (A/p, M) is a C^infty-subgroupoid of (A, M). Regarding this result a more general class of differential equations with generalized total differential are defined on the Lie algebroid L(A/p) with values in the Lie algebroid of a Lie groupoid (|Omega, ?). Moreover some specific examples of this approach along with a triviality criterion for groupoids are given such as the differential equations with total / logarithmic differential and values in Lie algebras in the case that A=M|times M and B={pt}. (This paper is based on a talk presented by the author in the 4th Panellenic Conference on Geometry on "Research in Geometry and in its Teaching towards the 21st century'' taking place in the University of Patras, Greece, 28-30 May 1999.)

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 44
Περίοδος	2000
Συγγραφέας	Apostolos N. Nikolopoulos
Αρ. Αρθρου	13
Σελίδες	117-127
Γλώσσα	-
Λέξεις Κλειδιά	Lie algebroids, Lie groupoids

On Differential Equations in lie Algebroids