Ver\"anderungen \"uber einen Satz von Timmesfeld - II. Symmetric powers of Nat sl(2,K)

TL;DR

This paper characterizes certain polynomial spaces within sl(2,K) representations, focusing on constructing compatible linear structures on abstract modules, advancing understanding of Lie ring modules.

Contribution

It introduces a method to identify polynomial spaces in sl(2,K) representations and constructs compatible linear structures on abstract modules, extending prior work on Lie ring representations.

Findings

Identification of polynomial spaces within sl(2,K) representations

Construction of compatible K-linear structures on abstract modules

Advancement in understanding Lie ring module structures

Abstract

We identify the spaces of homogeneous polynomials in two variables K[Y^k, XY^{k-1}, ..., X^k] among representations of the Lie ring sl(2,K). This amounts to constructing a compatible K-linear structure on some abstract sl(2,K)-modules, where sl(2,K) is viewed as a Lie ring.