Analytic decomposition of differential graded Lie algebras

Details Analytic decomposition of differential graded Lie algebras Analytic decomposition of differential graded Lie algebras

2006-07-31

arxiv.org/abs/math/0607764v1

Mathematics

Quantum Algebra

improves results of "Deformations of L-infinity algebras" (and intersects with it), includes convergence statements, 28 pages

Scientific paper

We prove explit formulas for the decomposition of a differential graded Lie algebra into a minimal and a linear $L_\infty$-algebra. We define a category of metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the structure maps satisfy a certain convergence condition and deduce a decomposition theorem for differential graded Lie algebras in this category. This theorem serves for instance to prove the convergence of the Kuranishi map assigned to a differential graded Lie algeba.

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