Classification of simple linearly compact Kantor triple systems over the complex numbers

TL;DR

This paper classifies all simple finite-dimensional linearly compact Kantor triple systems over the complex numbers using Satake diagrams, providing explicit descriptions for classical and exceptional cases.

Contribution

It offers a complete classification of simple linearly compact Kantor triple systems over complex numbers, including explicit presentations for all cases.

Findings

All simple linearly compact Kantor triple systems are finite-dimensional.

Explicit presentations for classical and exceptional systems are provided.

Classification is achieved via Satake diagrams.

Abstract

Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems.