A rank-three condition for invariant (1,2)-symplectic almost Hermitian structures on flag manifolds
type: Item
instance of: scholarly article
title: A rank-three condition for invariant (1,2)-symplectic almost Hermitian structures on flag manifolds
zbMATH Open document ID: 1016.22014
author: Nir Cohen
author: Caio J. C. Negreiros
author: Luiz A. B. San Martin
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2003-08-07T00:00:00Z
review text: The authors consider invariant \((1,2)\)-symplectic almost Hermitian structures on the maximal flag manifold associated to a complex semi-simple Lie group \(G\). An invariant almost complex structure \(J\) is called \((1,2)\)-admissible if there exists an invariant Riemannian metric \(\Lambda\) such that \((J, \Lambda)\) is \((1,2)\)-symplectic. It is shown that a \((1,2)\)-admissible almost complex structure is necessarily cone-free. The property of being cone-free is a condition on the rank three subsystems of the root system of \(G\) if this is not \(G_{2}\). It extends the property of being cone-free for tournaments related to the \( Sl(n,\mathbb{C})\) case [see \textit{N. Cohen, C. J. C. Negreiros} and \textit{L. A. B. San Martin}, Bull. Lond. Math. Soc. 34, No. 6, 641-649 (2002)]. If the semi-simple Lie group does not contain components of type \(B_{l}\), \(l \geq 3, G_{2}, F_{4}\), then this property is also sufficient.
reviewed by: Evangelia Samiou
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 1890487
zbMATH Keywords: semi-simple Lie groups
zbMATH Keywords: flag manifolds
zbMATH Keywords: affine Weyl groups
zbMATH Keywords: Hermitian geometry
MaRDI profile type: Publication
full work available at URL: s005740200002
OpenAlex ID: W2047924094
DOI: 10.1007/S005740200002
description: scientific article; zbMATH DE number 1890487