  Altermagnetism, a type of magnetic order that combines properties of
ferromagnets and antiferromagnets, has generated significant interest recently,
in particular due to its potential spintronics applications. Here, we show that
altermagnetic states, which typically involve collinear magnetic order of SU(2)
spins, can be generalized to higher SU($N$) symmetry groups. We construct a
two-dimensional Heisenberg model for a three-sublattice SU(3) altermagnet and
analyze its excitation spectrum via flavor-wave theory. By deriving a general
formula for the chirality of the excitations, we show that the SU(3)
altermagnet harbors chiral magnons that are split in energy. We also compute
the electronic band structure for a metallic system of the same symmetry and
map out the polarization of the resulting flavor-split bands. We conclude by
discussing further generalizations.
