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Deformations and the koherence

Markl, Martin (1994)

Proceedings of the Winter School "Geometry and Physics"

The cotangent cohomology of S. Lichtenbaum and M. Schlessinger [Trans. Am. Math. Soc. 128, 41-70 (1967; Zbl 0156.27201)] is known for its ability to control the deformation of the structure of a commutative algebra. Considering algebras in the wider sense to include coalgebras, bialgebras and similar algebraic structures such as the Drinfel’d algebras encountered in the theory of quantum groups, one can model such objects as models for an algebraic theory much in the sense of F. W. Lawvere [Proc....

Deformations of Lie brackets: cohomological aspects

Marius Crainic, Ieke Moerdijk (2008)

Journal of the European Mathematical Society

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.

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