ScholarLens Back to search
2003•arXiv (Cornell University)Open access

On Commutative Polarizations

Alexader G. Elashvili, Alfons I. Ooms

Open full text 0 citations

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.

Open-access reader

About this research paper

What this paper is about

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.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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.

Key concepts: Commutative property, Political science, Law and economics, Business, Mathematics, Sociology, Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Commutative Polarizations — Research Paper | ScholarLens