We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme X, and a coherent sheaf of Lie OX-algebras L, we determine the obstruction to the existence of extensions 0→L→E→Q→0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.
Lie algebroid cohomology and Lie algebroid extensions / Aldrovandi, E.; Bruzzo, U.; Rubtsov, V.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 505:(2018), pp. 456-481. [10.1016/j.jalgebra.2018.03.018]
Lie algebroid cohomology and Lie algebroid extensions
Aldrovandi, E.Membro del Collaboration group
;Bruzzo, U.
Membro del Collaboration group
;Rubtsov, V.Membro del Collaboration group
2018-01-01
Abstract
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme X, and a coherent sheaf of Lie OX-algebras L, we determine the obstruction to the existence of extensions 0→L→E→Q→0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.| File | Dimensione | Formato | |
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