\'{E}tale difference algebraic groups

TL;DR

This paper introduces a Jordan-Hölder type decomposition for tale difference algebraic groups, showing they can be constructed from simple tale algebraic groups and two finite tale difference algebraic groups, with a focus on their uniqueness properties.

Contribution

It establishes a novel decomposition theorem for tale difference algebraic groups, extending classical algebraic group theory into the difference algebra setting.

Findings

Decomposition of tale difference algebraic groups into simple components

Identification of two finite tale difference algebraic groups involved in the structure

Proof of a uniqueness property for the simple components

Abstract

\'{E}tale difference algebraic groups are a difference analog of \'{e}tale algebraic groups. Our main result is a Jordan-H\"{o}lder type decomposition theorem for these groups. Roughly speaking, it shows that any \'{e}tale difference algebraic group can be build up from simple \'{e}tale algebraic groups and two finite \'{e}tale difference algebraic groups. The simple \'{e}tale algebraic groups occurring in this decomposition satisfy a certain uniqueness property.