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Gauge equivalence for complete L-algebras

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<mark>Journal publication date</mark>7/07/2021
<mark>Journal</mark>Homology, Homotopy and Applications
Issue number2
Number of pages15
Pages (from-to)283-297
Publication StatusPublished
<mark>Original language</mark>English


We introduce a notion of left homotopy for Maurer–Cartan elements in L‑algebras and A‑algebras, and show that it corresponds to gauge equivalence in the differential graded case. From this we deduce a short formula for gauge equivalence, and provide an entirely homotopical proof to Schlessinger–Stasheff’s theorem. As an application, we answer a question of T. Voronov, proving a non-abelian Poincaré lemma for differential forms taking values in an L‑algebra.