On Commutative Polarizations

2003/02/19 by Alexader G. Elashvili, Elashvili, Alexader G., Alfons I. Ooms +1
Mathematics · #17B45 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B45

paper · pdf · doi:10.48550/arxiv.math/0302229

34 pages, 2 figures. Submitted to Journal of Algebra

arxiv created 2003/02/19 · openalex publication_date 2003/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study finite-dimensional Lie algebras over a field k of characteristic zero which admit a commutative polarization (CP). Among the many results and examples, it is shown that, if k is algebraically closed, the nilradical N of a parabolic subalgebra in A_n and C_n has such a CP. Using this fact a simple closed formula is derived for the index of N.

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