Unimodular group
This article defines a property that can be evaluated for a topological group (usually, a T0 topological group)
View a complete list of such properties
Definition
A unimodular group is a locally compact group satisfying the following equivalent conditions:
- Every left Haar measure is a right Haar measure.
- Every right Haar measure is a left Haar measure.
- There is a bi-invariant Haar measure on the group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| locally compact abelian group | |FULL LIST, MORE INFO | |||
| compact group | |FULL LIST, MORE INFO | |||
| discrete group | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| locally compact group |