Ver\"anderungen \"uber einen Satz von Timmesfeld - I. Quadratic Actions

TL;DR

This paper classifies quadratic modules for SL(2,K) and sl(2,K), extending previous results and laying groundwork for linearization of modules in algebraic group theory.

Contribution

It generalizes a theorem on quadratic SL(2,K)- and sl(2,K)-modules, providing a classification that advances understanding of modules for algebraic groups and Lie rings.

Findings

Crude classification of quadratic modules for SL(2,K) and sl(2,K)

Extension of Timmesfeld's theorem on module classification

Foundation for linearization of modules in algebraic groups

Abstract

We classify quadratic SL(2,K)- and sl(2,K)-modules by crude computation, generalizing in the first case a Theorem proved independently by F.-G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearization results for abstract modules of algebraic groups and associated Lie rings.