Hyperstructures of Affine Algebraic Group Schemes

TL;DR

This paper introduces hyperstructures on affine algebraic group schemes, extending classical group concepts via Hopf algebra structures, and generalizes previous work by Connes and Consani.

Contribution

It defines hyperstructures on affine algebraic groups using Hopf algebra structures, broadening the algebraic framework of group schemes.

Findings

Hyperstructures are canonically defined by Hopf algebra structures.

The approach generalizes classical group structures.

Partial generalization of Connes and Consani's results.

Abstract

We impose a rather unknown algebraic structure called a `hyperstructure' to the underlying space of an affine algebraic group scheme. This algebraic structure generalizes the classical group structure and is canonically defined by the structure of a Hopf algebra of global sections. This paper partially generalizes the result of A.Connes and C.Consani