Vector groupoid and Isometries

Abstract

The concept of groupoid considers as a generalization of the concept ofgroup, and the notion of an action of groupoid generalizes the action ofgroup relative to a bundle. In this paper we present the concept ofgroupoid into linear algebra using a structure of vector space, thisgroupoid namely " vector groupoid ". The purpose of this paper is toinvestigate many properties of vector groupoid comparable with thatsatisfy for groupoid in algebraic case ; also , we study these properties ina topological case using the concept of topological vector groupoid.Key words : Groupoid , Vector bundle , Isometries , Action of top. group and top.groupoid