We construct a family of groups from suitable higher rank graphs which are dimensional generalizations the Thompson groups. introduce group invariants, inspired by K-theory C⁎-algebras, and show that many our not isomorphic to Brin-Thompson nV, when n≥2.

We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems.