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# Algebra bundle

V. de Paiva. "A dialectica-like model of linear logic". In Proc. Conf. on Category Theory and Computer Science, Springer-Verlag Lecture Notes in Computer Science 389, pp. 341–356, Manchester, September 1989.

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

Lie algebra bundle

References

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.

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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