Algebra bundle
From Wikipedia, the free encyclopedia
Page Module:Message box/ambox.css has no content.
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2024) |
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-algebra bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as well as the Clifford bundle associated to any Riemannian vector bundle.
See also
References
- Page Module:Citation/CS1/styles.css has no content.Greub, Werner; Halperin, Stephen; Vanstone, Ray (1973), Connections, curvature, and cohomology. Vol. II: Lie groups, principal bundles, and characteristic classes, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, MR 0336651.
- Page Module:Citation/CS1/styles.css has no content.Chidambara, C.; Kiranagi, B. S. (1994), "On cohomology of associative algebra bundles", Journal of the Ramanujan Mathematical Society, 9 (1): 1–12, MR 1279097.
- Page Module:Citation/CS1/styles.css has no content.Kiranagi, B. S.; Rajendra, R. (2008), "Revisiting Hochschild cohomology for algebra bundles", Journal of Algebra and Its Applications, 7 (6): 685–715, doi:10.1142/S0219498808003041, MR 2483326.
- Page Module:Citation/CS1/styles.css has no content.Kiranagi, B.S.; Ranjitha, Kumar; Prema, G. (2014), "On completely semisimple Lie algebra bundles", Journal of Algebra and Its Applications, 14 (2): 1–11, doi:10.1142/S0219498815500097.
