Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras
type: Item
instance of: scholarly article
title: Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras
zbMATH Open document ID: 1300.17009
author: Michael Gulde
author: Markus Stroppel
published in: Linear Algebra and its Applications
publication date: 2012-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.0502
review text: The authors study nilpotent Lie algebras \(L\) of class 2 with the property that \(\dim (L/[L,L]) =4\). Algebras of this type were classified by the second author in [J. Lie Theory 18, No. 2, 391--411 (2008; Zbl 1179.17013)] by a geometric approach using the action of \(\mathrm{GL}(L/[L,L])\) on the Klein quadric. In the paper under review, the authors use the same setting to determine the automorphism group \(\Aut(L)\) of \(L\) and the orbits of \(\Aut(L)\) on \(L\).
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 6053093
zbMATH Keywords: Klein quadric
zbMATH Keywords: Grassmann space
zbMATH Keywords: automorphism
zbMATH Keywords: orbit
zbMATH Keywords: nilpotent Lie algebra
zbMATH Keywords: Heisenberg algebra
zbMATH Keywords: quadratic field extension
zbMATH Keywords: quaternion algebra
MaRDI profile type: Publication
OpenAlex ID: W2127342311
arXiv ID: 1012.0502
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DOI: 10.1016/J.LAA.2012.03.018
description: scientific article; zbMATH DE number 6053093