Semi-inner product structures for groupoids

TL;DR

This paper introduces semi-inner product structures for groupoids, extending the concept of inner products from vector spaces to the more general setting of groupoids, and explores their properties as groupoid norms.

Contribution

It defines semi-inner products for groupoids, establishing a new framework that generalizes inner products to a broader algebraic context.

Findings

Defines scalar valued groupoid bihomomorphisms

Shows these bihomomorphisms satisfy axioms similar to groupoid norms

Establishes foundational properties of semi-inner products for groupoids

Abstract

In this paper there are considered some scalar valued groupoid bihomomorphism structures, being in fact the groupoid counterparts of the inner product notion originally defined for vectors. These bihomomorphisms, called here the semi-inner products for groupoids, determine non-negative real valued functions which fulfill the axioms assumed for a groupoid norm concept [2].