Some results on certain finite-dimensional subalgebras of the hyperalgebra of a universal Chevalley group

TL;DR

This paper investigates specific subalgebras within the hyperalgebra of Frobenius kernels of universal Chevalley groups over fields with positive characteristic, focusing on cases with small primes and non-simply-laced diagrams.

Contribution

It provides new results on the structure of certain finite-dimensional subalgebras in hyperalgebras under special conditions.

Findings

Identification of particular subalgebras generated by specific subsets.

Results on the structure when the characteristic p is very small.

Insights into the case of non-simply-laced Dynkin diagrams.

Abstract

In the hyperalgebra of the $r$-th Frobenius kernel of a universal Chevalley group over a field of characteristic $p>0$, we study some subsets and the subalgebras generated by them and give some results. We are particularly interested in the case that $p$ is 'very small' and the Dynkin diagram is not simply-laced.