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:

    “The question of whether it’s God’s green earth is not at center stage, except in the sense that if so, one is reminded with some regularity that He may be dying.”
    —Edward Hoagland (b. 1932)

    “I don’t think America’s the center of the world anymore. I think African women will lead the way [in] ... women’s liberation ... The African woman, she’s got a country, she’s got the flag, she’s got her own army, got the navy. She doesn’t have a racism problem. She’s not afraid that if she speaks up, her man will say goodbye to her.”
    —Faith Ringgold (b. 1934)

    “Whether talking about addiction, taxation [on cigarettes] or education [about smoking], there is always at the center of the conversation an essential conundrum: How come we’re selling this deadly stuff anyway?”
    —Anna Quindlen (b. 1952)