2018年4月25日
Pseudo-metric 2-step nilpotent Lie algebras
Advances in Geometry
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- ,
- ,
- 巻
- 18
- 号
- 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.
- ID情報
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- DOI : 10.1515/advgeom-2017-0051
- ISSN : 1615-715X
- SCOPUS ID : 85045663513