This entry is about items in the ADE-classification labeled by $D4$. For the D4-brane, see there.
In the ADE-classification, the items labeled $D4$ include the following:
the Klein four-group (the smallest dihedral group)
$\mathbb{Z}/2 \times \mathbb{Z}/2$
the quaternion group of order 8 (the smallest binary dihedral group):
$Q_8 \simeq 2 D_4$
as simple Lie groups: the special orthogonal group in 8 dimensions
as a Dynkin diagram/Dynkin quiver:
The S3-symmetry group of the D4-diagram translates into interesting 3-fold symmetries of structures associated with the corresponding objects in the above list. This is known as triality.
ADE classification and McKay correspondence
Last revised on August 29, 2019 at 13:45:57. See the history of this page for a list of all contributions to it.