Geodesic
The Atiyah Extension of a Lie Algebra Deformation
Journal of Lie theory, Tome 15 (2005) no. 2, pp. 497-503 Cet article a éte moissonné depuis la source Heldermann Verlag

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\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.
Classification : 32G99, 17B55, 14D14
Mots-clés : Sheaf of Lie algebras, deformation, Atiyah class, extension of Lie algebras 
@article{JLT_2005_15_2_JLT_2005_15_2_a7,
     author = {Z. Ran },
     title = {The {Atiyah} {Extension} of a {Lie} {Algebra} {Deformation}},
     journal = {Journal of Lie theory},
     pages = {497--503},
     year = {2005},
     volume = {15},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a7/}
}
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Z. Ran . The Atiyah Extension of a Lie Algebra Deformation. Journal of Lie theory, Tome 15 (2005) no. 2, pp. 497-503. http://geodesic.mathdoc.fr/item/JLT_2005_15_2_JLT_2005_15_2_a7/