Dabkowski, Mieczyslaw K.; Herzig, Emily; Ramakrishna, Viswanath Inversion of double-covering map \(SPIN(N) \to SO (N, {\mathbb R})\) for \(N \leq 6\). (English) Zbl 1376.22012 J. Geom. Symmetry Phys. 42, 15-51 (2016). For any integer \(n\), the spin group \(\text{Spin}(n)\) is the double cover of the special orthogonal group \(\text{SO}(n,\mathbb{R})\) such that there is a short exact sequence of Lie groups \[ 1 \rightarrow \mathbb{Z}/2 \mathbb{Z} \rightarrow \text{Spin}(n) \rightarrow \text{SO}(n,\mathbb{R}) \rightarrow 1. \] The cases \(n=3\) and \(4\), where \(\text{Spin}(n)=\text{SU}(2)\) and \(\text{SU}(2) \times \text{SU}(2)\) respectively, are classical and date back to Hamilton, who described both the covering maps and the co-images using the quaternion algebra \(\mathbb{H}\).In the paper under discussion, the authors consider the cases \(n=5\) and 6, where \(\text{Spin}(n)=\text{Sp}(4)\) and \(\text{SU}(4)\) respectively. They provide explicit formulas for the covering maps, and algorithms for finding the co-images. Reviewer: Adam Chapman (Upper Galilee) MSC: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods 20G20 Linear algebraic groups over the reals, the complexes, the quaternions Keywords:Lie algebras; linear algebraic groups × Cite Format Result Cite Review PDF Full Text: DOI