Spin Group - Center

Center

The center of the spin groups (complex and real) are given as follows:

Z(\operatorname{Spin}(n,\mathbb{C})) = \begin{cases} \mathbb{Z}_2 & n = 2k+1\\ \mathbb{Z}_4 & n = 4k+2\\ \mathbb{Z}_2 \oplus \mathbb{Z}_2 & n = 4k\\ \end{cases}
Z(\operatorname{Spin}(p,q)) = \begin{cases} \mathbb{Z}_2 & n = 2k+1,\\ \mathbb{Z}_2 & n = 2k, \text{ and } p, q \text{ odd}\\ \mathbb{Z}_4 & n = 2k, \text{ and } p, q \text{ even}\\ \end{cases}

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