In mathematics, an algebra bundle is a fiber bundle whose fibers are algebras and local trivializations respect the algebra structure. It follows that the transition functions are algebra isomorphisms. Since algebras are also vector spaces, every algebra bundle is a vector bundle.
Examples include the tensor bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as well as the Clifford bundle associated to any Riemannian vector bundle.
Famous quotes containing the words algebra and/or bundle:
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“We styled ourselves the Knights of the Umbrella and the Bundle; for, wherever we went ... the umbrella and the bundle went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and bundle were.”
—Henry David Thoreau (1817–1862)