Semisimple algebras of vector fields on C^N of maximal rank

TL;DR

This paper classifies semisimple algebras of vector fields on complex N-space with maximal rank, using representation theory and canonical forms, advancing understanding of their structure.

Contribution

It provides a complete classification of such algebras, highlighting their structure and the role of Cartan subalgebras in their characterization.

Findings

Classification of semisimple vector field algebras on C^N

Use of representation theory in classification

Identification of local canonical forms

Abstract

A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local canonical form of semisimple Lie algebras of vector fields.