nLab structure group

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Group Theory

Bundles

bundles

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Idea

For GG a group and PP a GG-torsor, GG is also called the structure group of PP.

This usage is particularly common in the case that GG is a geometric group (e.g. a topological group or Lie group) and PXP \to X a GG-principal bundle.

More generally, and less tautologically, if VXV \to X is a GG-associated bundle then one says that VV has structure group GG.

In particular when V=TXV = T X is a tangent bundle with structure group GG one also says that XX 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.