Complete classification of pseudo H -type Lie algebras: I
作者: Kenro FurutaniIrina Markina
作者单位: 1Science University of Tokyo
2University of Bergen
刊名: Geometriae Dedicata, 2017, Vol.190 (1), pp.23-51
来源数据库: Springer Nature Journal
DOI: 10.1007/s10711-017-0225-1
关键词: Clifford moduleNilpotent 2-step Lie algebraPseudo H -type Lie algebrasLie algebra isomorphismScalar productPrimary 17B6017B3017B7022E15
原始语种摘要: Let \({\mathscr {N}}\) be a 2-step nilpotent Lie algebra endowed with a non-degenerate scalar product \(\langle .\,,.\rangle \) , and let \({\mathscr {N}}=V\oplus _{\perp }Z\) , where Z is the centre of the Lie algebra and V its orthogonal complement. We study classification of the Lie algebras for which the space V arises as a representation space of the Clifford algebra \({{\mathrm{{\mathrm{Cl}}}}}({\mathbb {R}}^{r,s})\) , and the representation map \(J:{{\mathrm{{\mathrm{Cl}}}}}({\mathbb {R}}^{r,s})\rightarrow {{\mathrm{End}}}(V)\) is related to the Lie algebra structure by \(\langle J_zv,w\rangle =\langle z,[v,w]\rangle \) for all \(z\in {\mathbb {R}}^{r,s}\) and \(v,w\in V\) . The classification depends on parameters r and s and is completed for the Clifford modules V having minimal...
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影响因子:0.465 (2012)

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关键词翻译
关键词翻译
  • algebra 代数学
  • classification 分类
  • isomorphism 同晶型
  • isomorphic 同形的
  • representation 表现
  • constructive 建设的
  • proof 证明
  • degenerate 退化
  • pseudo 
  • parameters 参数