論文

査読有り
2018年4月25日

Pseudo-metric 2-step nilpotent Lie algebras

Advances in Geometry
  • Christian Autenried
  • ,
  • Kenro Furutani
  • ,
  • Irina Markina
  • ,
  • Alexander Vasiév

18
2
開始ページ
237
終了ページ
263
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1515/advgeom-2017-0051
出版者・発行元
Walter de Gruyter GmbH

The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that a 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step nilpotent Lie algebra endowed with some standard non-degenerate scalar product compatible with the Lie bracket. This choice of the standard pseudo-metric form allows us to study the isomorphism properties. If the elements of the centre of the standard pseudo-metric form constitute a Lie triple system of the pseudo-orthogonal Lie algebra, then the original 2-step nilpotent Lie algebra admits integer structure constants. Among particular applications we prove that pseudo H-type algebras have bases with rational structure constants, which implies that the corresponding pseudo H-type groups admit lattices.

リンク情報
DOI
https://doi.org/10.1515/advgeom-2017-0051
ID情報
  • DOI : 10.1515/advgeom-2017-0051
  • ISSN : 1615-715X
  • SCOPUS ID : 85045663513

エクスポート
BibTeX RIS