# nLab exceptional spinors and division algebras -- table

exceptional spinors and real normed division algebras

Lorentzian
spacetime
dimension
$\phantom{AA}$spin groupnormed division algebra$\,\,$ brane scan entry
$3 = 2+1$$Spin(2,1) \simeq SL(2,\mathbb{R})$$\phantom{A}$ $\mathbb{R}$ the real numberssuper 1-brane in 3d
$4 = 3+1$$Spin(3,1) \simeq SL(2, \mathbb{C})$$\phantom{A}$ $\mathbb{C}$ the complex numberssuper 2-brane in 4d
$6 = 5+1$$Spin(5,1) \simeq$ SL(2,H)$\phantom{A}$ $\mathbb{H}$ the quaternionslittle string
$10 = 9+1$Spin(9,1) ${\simeq}$SL(2,O)$\phantom{A}$ $\mathbb{O}$ the octonionsheterotic/type II string

Last revised on April 6, 2021 at 03:29:57. See the history of this page for a list of all contributions to it.