A geometrical approach to g-digroups

Authors:
Preprint
Publisher website
Google Scholar
Abstract
Representation group theory plays an important role in group theory, much more in geometry, on which we can determine, in many cases, what kind of geometry or geometries a manifold M supports by knowing a faithful representation of the fundamental group Π1(M) in the group Iso + (M) of preserving-orientations isometries of M. Motivated by this and by the definition of a g-digroup action given in [1], in this paper we present a study of such action by proving some interesting results that are well known in group actions, for example: the orbit stabilizer theorem, the class equation, Burnside’s formula and we relate g-digroup actions with trioids. We introduce the definition of representation of a g-digroup into dialge-bras and a strong connection with g-digroup action, like in the case of group. We present the g-digroups as an invariant of quotient orbifolds.

This publication has 15 references indexed in Scilit: