Journal of Lie Theory

no. 2
The Atiyah Extension of a Lie Algebra Deformation
Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 497-503
\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.
DOI: 10.5802/jolt.387
Classification: 32G99, 17B55, 14D14
Keywords: Sheaf of Lie algebras, deformation, Atiyah class, extension of Lie algebras 
@article{JOLT_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},
     doi = {10.5802/jolt.387},
     zbl = {1082.32012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.387/}
}
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Z. Ran. The Atiyah Extension of a Lie Algebra Deformation. Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 497-503. doi: 10.5802/jolt.387

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