Open Access
2016 Inversion of Double-Covering Map $\mathrm{Spin}(n) \rightarrow \mathrm{SO}(n, {\mathbb{R}})$ for $n\leq 6$
Mieczyslaw K. Dabkowski, Emily Herzig, Viswanath Ramakrishna
J. Geom. Symmetry Phys. 42: 15-51 (2016). DOI: 10.7546/jgsp-42-2016-15-51


This work provides an algorithmic procedure for finding the pair of elements in the spin group which map to a given matrix in the special orthogonal group of order five or six. This is achieved by first solving the problem when the special orthogonal matrix is a Givens rotation, and then exploiting the fact that the covering maps are group homomorphisms and that any special orthogonal matrix can be explicitly decomposed into a product of Givens rotations. For this purpose systems of quadratic equations in several variables have to be solved symbolically. The resulting solution display a transparent dependency on the entries of the Givens matrices.


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Mieczyslaw K. Dabkowski. Emily Herzig. Viswanath Ramakrishna. "Inversion of Double-Covering Map $\mathrm{Spin}(n) \rightarrow \mathrm{SO}(n, {\mathbb{R}})$ for $n\leq 6$." J. Geom. Symmetry Phys. 42 15 - 51, 2016.


Published: 2016
First available in Project Euclid: 31 May 2017

zbMATH: 1376.22012
MathSciNet: MR3586442
Digital Object Identifier: 10.7546/jgsp-42-2016-15-51

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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