Unimodular group

Summary

A unimodular group is a locally compact group whose left Haar measure is also right-invariant, that is, whose modular function is identically $1$. Abelian groups, compact groups, discrete groups, semisimple Lie groups and connected nilpotent Lie groups are unimodular. Many results of harmonic analysis, such as the existence of lattices or the simplest form of trace formulas, require unimodularity.