Restricted infinitesimal deformations of restricted simple Lie algebras

TL;DR

This paper calculates the restricted infinitesimal deformations of restricted simple Lie algebras over algebraically closed fields with characteristic not equal to 2 or 3, advancing understanding of their structural flexibility.

Contribution

It provides the first comprehensive computation of restricted infinitesimal deformations for these Lie algebras, filling a gap in the algebraic deformation theory.

Findings

Explicit descriptions of deformation spaces obtained

Deformations characterized for all restricted simple Lie algebras in the specified characteristic

New insights into the rigidity and flexibility of these algebraic structures

Abstract

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.