Primitive idempotents of the hyperalgebra for the $r$-th Frobenius kernel of ${\rm SL}(2,k)$

TL;DR

This paper constructs primitive idempotents within the hyperalgebra associated with the r-th Frobenius kernel of SL(2,k), advancing understanding of its algebraic structure.

Contribution

It provides an explicit construction of primitive idempotents for the hyperalgebra of the Frobenius kernel of SL(2,k), a novel contribution to algebraic group theory.

Findings

Explicit primitive idempotents constructed

Enhanced understanding of hyperalgebra structure

Potential applications in representation theory

Abstract

In this paper we construct primitive idempotents of the hyperalgebra for the $r$-th Frobenius kernel of the algebraic group ${\rm SL}(2,k)$.