
Journal of Lie Theory 15 (2005), No. 2, 497503 Copyright 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 [Abstractpdf] \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 [ Fulltextpdf (145 KB)] for subscribers only. 