Geodesic
Gauge equivalence for complete $L_\infty$-algebras
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 283-297.

Voir la notice de l'article provenant de la source International Press of Boston

We introduce a notion of left homotopy for Maurer–Cartan elements in $L_\infty$‑algebras and $A_\infty$‑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 $L_\infty$‑algebra.
DOI : 10.4310/HHA.2021.v23.n2.a15
Classification : 17B55, 18G55
Keywords: Maurer–Cartan element, differential graded Lie algebra, homotopy, model category, deformation 
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     author = {Ai Guan},
     title = {Gauge equivalence for complete $L_\infty$-algebras},
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     pages = {283--297},
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     year = {2021},
     doi = {10.4310/HHA.2021.v23.n2.a15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a15/}
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Ai Guan. Gauge equivalence for complete $L_\infty$-algebras. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 283-297. doi : 10.4310/HHA.2021.v23.n2.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a15/

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