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Cayley transform, outer exponential and spinor norm. (English) Zbl 0652.15022

Geometry and physics, Proc. Winter Sch., Srnî/Czech. 1987, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 16, 191-198 (1987).
[For the entire collection see Zbl 0634.00015.]
The Cayley transform of an antisymmetric \(n\times n\) matrix A is the rotation matrix \(U=(I+A)(I-A)^{-1}\) in SO(n). A new proof of the following theorem is given: \(Ux=s^{-1}xs\), where \(s=e^{\Lambda B}\) is the unique element in the Lipschitz group \(\Gamma_ n\) (the group of invertible elements of the Clifford algebra \({\mathbb{R}}_ n)\), and the matrices A and U correspond to the bivector B in \({\mathbb{R}}^ 2_ n\), \(Ax=x\cdot B\).
Reviewer: W.Wiesław

MSC:

15A66 Clifford algebras, spinors
53C27 Spin and Spin\({}^c\) geometry

Citations:

Zbl 0634.00015
Full Text: EuDML