Editing Algebra bundle

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In [[mathematics]], an '''algebra bundle''' is a [[fiber bundle]] whose [[fiber (mathematics)|fiber]]s are [[algebra over a field|algebra]]s and [[local trivialization]]s respect the algebra structure. It follows that the [[Transition map|transition functions]] are [[algebra isomorphism]]s. Since algebras are also [[vector space]]s, 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==
*{{citation
 | last1 = Greub | first1 = Werner
 | last2 = Halperin | first2 = Stephen
 | last3 = Vanstone | first3 = Ray
 | mr = 0336651
 | publisher = Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London
 | title = Connections, curvature, and cohomology. Vol. II: Lie groups, principal bundles, and characteristic classes
 | year = 1973}}.
*{{citation
 | last1 = Chidambara | first1 = C.
 | last2 = Kiranagi | first2 = B. S.
 | issue = 1
 | journal = Journal of the Ramanujan Mathematical Society
 | mr = 1279097
 | pages = 1–12
 | title = On cohomology of associative algebra bundles
 | volume = 9
 | year = 1994}}.
*{{citation
 | last1 = Kiranagi | first1 = B. S.
 | last2 = Rajendra | first2 = R.
 | doi = 10.1142/S0219498808003041
 | issue = 6
 | journal = Journal of Algebra and Its Applications
 | mr = 2483326
 | pages = 685–715
 | title = Revisiting Hochschild cohomology for algebra bundles
 | volume = 7
 | year = 2008}}.
*{{citation
 | last1=Kiranagi | first1=B.S.
 | last2= Ranjitha | first2 =Kumar  
 | last3=Prema | first3= G.
 | doi= 10.1142/S0219498815500097
 | issue = 2
 | journal = Journal of Algebra and Its Applications  
 | pages = 1–11 
 | title = On completely semisimple Lie algebra bundles
 |volume=14 
 | year = 2014}}.

[[Category:Vector bundles]]


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