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}

Read more about this topic:  Spin Group

Famous quotes containing the word center:

    “My center is giving way, my right is in retreat; situation excellent. I shall attack.”
    —Ferdinand Foch (1851–1929)

    “This is a strange little complacent country, in many ways a U.S.A. in miniature but of course nearer the center of disturbance!”
    —Eleanor Roosevelt (1884–1962)

    “When the landscape buckles and jerks around, when a dust column of debris rises from the collapse of a block of buildings on bodies that could have been your own, when the staves of history fall awry and the barrel of time bursts apart, some turn to prayer, some to poetry: words in the memory, a stained book carried close to the body, the notebook scribbled by hand—a center of gravity.”
    —Adrienne Rich (b. 1929)