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  "body": "\n## Summary\n\nA unimodular group is a [[locally compact group|AHV05ZBCYW]] whose left [[Haar measure|VY0HXD3GC4]] is also right-invariant, that is, whose [[modular function|63TX60RTRQ]] is identically $1$.\nAbelian groups, compact groups, discrete groups, semisimple Lie groups and connected nilpotent Lie groups are unimodular.\nMany results of harmonic analysis, such as the existence of lattices or the simplest form of trace formulas, require unimodularity.\n\n## Explanations\n\n### L1 human\n\nIn some groups, measuring sizes in a way that ignores left shifts automatically ignores right shifts as well.\nThese groups are called unimodular.\nCommutative groups are the obvious example, because left and right shifts agree.\nThe group of affine maps $x \\mapsto ax + b$ with $a \u003e 0$ is the standard group that is not unimodular: its left and right Haar measures are $da \\, db / a^2$ and $da \\, db / a$.\n",
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