Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
vector bundle, 2-vector bundle, (∞,1)-vector bundle
real, complex/holomorphic, quaternionic
For a group and a -torsor, is also called the structure group of .
This usage is particularly common in the case that is a geometric group (e.g. a topological group or Lie group) and a -principal bundle.
More generally, and less tautologically, if is a -associated bundle then one says that has structure group .
In particular when is a tangent bundle with structure group one also says that is equipped with G-structure.
In physics, with these bundles understood as field bundles (cf. fiber bundles in physics) the structure group is called the gauge group.
Last revised on June 25, 2024 at 14:30:40. See the history of this page for a list of all contributions to it.