MODULES WITH IN THE SPACE OF ALL DERIVATIONS OF AN ALGEBRA

Authors : H. ABBASI, GH.HAGHIGHATDOOST

Pages : 1-18

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Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :In this paper, we construct a groupoid associated to a modulewith values in the space of all derivations of a unital algebra. More precisely,for a pair insert ignore into journalissuearticles values(A, G); consisting of an algebra A with a unit, a module G over thecenter Zinsert ignore into journalissuearticles values(A); of A together with a homomorphism of Zinsert ignore into journalissuearticles values(A);-modules from G tothe space of all derivations Derinsert ignore into journalissuearticles values(A); of A, we associate a groupoid. We discusson the equivalence relation induced from this groupoid
Keywords : Groupoid, Lie algebra, Lie algebroid