Deformation of infinite dimensional differential graded Lie algebras

doi:https://doi.org/10.48550/arxiv.hep-th/9411070

Open AccessPreprint10.48550/arxiv.hep-th/9411070

Deformation of infinite dimensional differential graded Lie algebras

Maxim Braverman-1994-11-10-arXiv (Cornell University)

TL;DRAbstract

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc. For elliptic differential graded algebra we construct a complete set of deformations. We show that for several deformation problems the existence of a formal power series solution guarantees the existence of an analytic solution.

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We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc. For elliptic differential graded algebra we construct a complete set of deformations. We show that for several deformation problems the existence of a formal power series solution guarantees the existence of an analytic solution.

Keywords

Deformation (meteorology)Differential (mechanical device)Lie algebraMathematicsPure mathematicsPhysicsAlgebra over a field

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