On the dimension of the sheets of a reductive Lie algebra

TL;DR

This paper corrects a previous result on the dimension of sheets in reductive Lie algebras, confirming its validity using recent mathematical developments despite earlier identified errors.

Contribution

It provides a corrigendum to a prior theorem, validating its correctness through recent results by Premet and Topley.

Findings

Theorem 25 remains correct despite earlier errors.

Recent results support the original theorem's validity.

The correction clarifies the dimension of sheets in reductive Lie algebras.

Abstract

This note is a corrigendum to the previous version arXiv:0711.2735v3 published in J. Lie Theory. As it has been recently pointed out to me by Alexander Premet, Remark 3 of arXiv:0711.2735v3 is incorrect. We verify in this note thanks to recent results of Premet and Topley (see arXiv:1301.4653) that Theorem 25 of arXiv:0711.2735v3 remains correct in spite of this error.