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Gauge equivalence for complete L∞-algebras

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Gauge equivalence for complete L∞-algebras. / Guan, Ai.
In: Homology, Homotopy and Applications, Vol. 23, No. 2, 07.07.2021, p. 283-297.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Guan, A 2021, 'Gauge equivalence for complete L∞-algebras', Homology, Homotopy and Applications, vol. 23, no. 2, pp. 283-297. https://doi.org/10.4310/HHA.2021.v23.n2.a15

APA

Guan, A. (2021). Gauge equivalence for complete L∞-algebras. Homology, Homotopy and Applications, 23(2), 283-297. https://doi.org/10.4310/HHA.2021.v23.n2.a15

Vancouver

Guan A. Gauge equivalence for complete L∞-algebras. Homology, Homotopy and Applications. 2021 Jul 7;23(2):283-297. doi: 10.4310/HHA.2021.v23.n2.a15

Author

Guan, Ai. / Gauge equivalence for complete L∞-algebras. In: Homology, Homotopy and Applications. 2021 ; Vol. 23, No. 2. pp. 283-297.

Bibtex

@article{9602b85adfcd462187d3853135e8107b,
title = "Gauge equivalence for complete L∞-algebras",
abstract = "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{\textquoteright}s theorem. As an application, we answer a question of T. Voronov, proving a non-abelian Poincar{\'e} lemma for differential forms taking values in an L∞‑algebra.",
author = "Ai Guan",
year = "2021",
month = jul,
day = "7",
doi = "10.4310/HHA.2021.v23.n2.a15",
language = "English",
volume = "23",
pages = "283--297",
journal = "Homology, Homotopy and Applications",
issn = "1532-0073",
publisher = "International Press of Boston, Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Gauge equivalence for complete L∞-algebras

AU - Guan, Ai

PY - 2021/7/7

Y1 - 2021/7/7

N2 - 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.

AB - 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.

U2 - 10.4310/HHA.2021.v23.n2.a15

DO - 10.4310/HHA.2021.v23.n2.a15

M3 - Journal article

VL - 23

SP - 283

EP - 297

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 2

ER -