Analytic decomposition of differential graded Lie algebras

Abstract

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.

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