Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 15 (2005), No. 2, 497--503Copyright Heldermann Verlag 2005 The Atiyah Extension of a Lie Algebra Deformation Ziv Ran University of California, Dept. of Mathematics, Riverside CA 92521, U.S.A. ziv.ran@ucr.edu [Abstract-pdf] \def\g{{\frak g}} We construct an analogue of the Atiyah Class', or Atiyah Extension' in the context of deformation theory of sheaves of Lie algebras. Given a (suitable) sheaf $\g$ of Lie algebras on a space $X$, and a $\g$-deformation $\phi$ over a formally smooth base, our Atiyah Extension is a Lie algebra extension of the algebra of base vector fields by the $\phi$-twist of $\g$. It comes equipped with a representation of the $\phi$-twist on any (admissible) $\g$-module. Keywords: Sheaf of Lie algebras, deformation, Atiyah class, extension of Lie algebras. MSC: 32G99; 17B55, 14D14 [ Fulltext-pdf  (145  KB)] for subscribers only.