Spin Group - Center

Center

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

$Z(\operatorname{Spin}(n,\mathbb{C})) = \begin{cases} \mathbb{Z}_2 & n = 2k+1\\ \mathbb{Z}_4 & n = 4k+2\\ \mathbb{Z}_2 \oplus \mathbb{Z}_2 & n = 4k\\ \end{cases}$

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

Famous quotes containing the word center:

“Death is someone you see very clearly with eyes in the center of your heart: eyes that see not by reacting to light, but by reacting to a kind of a chill from within the marrow of your own life.”
—Thomas Merton (1915–1968)

“I am the center of the world, but the control panel seems to be somewhere else.”
—Mason Cooley (b. 1927)

“Columbus stood in his age as the pioneer of progress and enlightenment. The system of universal education is in our age the most prominent and salutary feature of the spirit of enlightenment, and it is peculiarly appropriate that the schools be made by the people the center of the day’s demonstration. Let the national flag float over every schoolhouse in the country and the exercises be such as shall impress upon our youth the patriotic duties of American citizenship.”
—Benjamin Harrison (1833–1901)