nLab
triality

Contents

Contents

Idea

The Dynkin diagram/Dynkin quiver D4 has an S3-symmetry group

(graphics grabbed from Wikipedia here)

This manifests itself in “triality” symmetries enjoyed by the objects that are labeled by D4 in an ADE-classification.

Specifically for the simple Lie group SO(8) corresponding to D4, triality is the statement that the two spin representations of the corresponding spin group Spin(8)Spin(8) and the defining vector representations are all isomorphic, and in a nice way.

References

See also

Last revised on March 31, 2019 at 09:22:52. See the history of this page for a list of all contributions to it.