Construcción de modelos de Gelfand grupoideales vía la máquina de Mackey para productos semidirectos de grupos finitos

Abstract

A. groupoid is the natural generalization of a group, considered as a category: it is a category where each morphism is invertible. In the present thesis we will use characters of the movements groupoid M(G, X), groupoid associated to the geometric pair (X, G) (G finite group), being able to construct a Gelfand model for G. The characters of M(G, X) allow to twist the natural representation of G, which supplies a Gelfand model for the G group. In particular, we present and prove that certain spaces X are from Gelfand (spaces whose twisted natural representation is a Gelfand model), this for certain classical groups, namely, Dihedral groups and rigid transformations groups associated with finites extensions onon finite fields. In order to give a general answer to the cardinal of such spaces of Gelfand, furthermore, to be able to present at least one candidate to be a Gelfand space for a certain group G= Ax H backed up by the Mackey machine and the construct that it makes regarding to the irreducible representations for G.