Advances in Applied Clifford Algebras

, Volume 21, Issue 4, pp 813–827 | Cite as

Triality Transformation and Lie Group Spin7

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Abstract

In this paper, we use Clifford algebras Cℓ 8 to study the triality transformation on group Spin(8). As application we study the Lie group Spin 7 and the related geometry on Grassmann manifolds. We also use Clifford algebras Cℓ(4, 4) to study the triality transformation on group Spin 0 (4, 4).

Mathematics Subject Classification (2010)

53C27 15A66 14M15 

Keywords

Clifford algebra Lie group Triality transformation Grassmann manifold 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of FoundationSuzhou Vocational UniversitySuzhouChina
  2. 2.Department of MathematicsSuzhou UniversitySuzhouChina

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