Pin(5)

- group, ∞-group
- group object, group object in an (∞,1)-category
- abelian group, spectrum
- group action, ∞-action
- representation, ∞-representation
- progroup
- homogeneous space

**spin geometry**, **string geometry**, **fivebrane geometry** …

**rotation groups in low dimensions**:

see also

The exceptional isomorphism Spin(5) $\simeq$ Sp(2) (this Prop.) generalizes to

$Pin^\pm(5)
\;\simeq\;
Sp(2)
\sqcup
\omega Sp(2)
\phantom{AAA}
\omega^2 = \pm e$

where $\omega \in Z\big( Pin^+(5)\big)$ is an element in the center which, for $Pin^+(5)$, squares to the the neutral element $e$ (corresponding to the Clifford algebra element $+1$) or, for $Pin^-(5)$, to $-e$ (the Clifford algebra element $-1$).

(e.g. Varlamov 99, Theorem 5)

**rotation groups in low dimensions**:

see also

- Vadim V. Varlamov,
*Fundamental Automorphisms of Clifford Algebras and an Extension of Dabrowski Pin Groups*, Hadronic J. 22 (1999) 497-533 (arXiv:math-ph/9904038v2)

Created on May 14, 2019 at 00:14:05. See the history of this page for a list of all contributions to it.