Algebra bundle
Nowadays, Algebra bundle is a topic of great importance in modern society. Its influence extends to various areas of daily life, from politics to technology, culture and economics. This article delves into the world of Algebra bundle, exploring its many facets and effects on our daily lives. Through a detailed analysis, we will seek to shed light on the different aspects that make Algebra bundle a relevant topic worthy of study today. From its impact on people's lives to its impact on the global environment, Algebra bundle is a phenomenon that deserves to be examined in depth.
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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
- Greub, Werner; Halperin, Stephen; Vanstone, Ray (1973), Connections, curvature, and cohomology. Vol. II: Lie groups, principal bundles, and characteristic classes, Academic Press , New York-London, MR 0336651.
- Chidambara, C.; Kiranagi, B. S. (1994), "On cohomology of associative algebra bundles", Journal of the Ramanujan Mathematical Society, 9 (1): 1–12, MR 1279097.
- 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.
- 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.
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