The gauge action, DG Lie algebras and identities for Bernoulli numbers

Buijs, U.;Carrasquel Vera, Jose Gabriel;Murillo, A.
(2017) Forum mathematicum — Vol. 29, n° 2, p. 277-286 (2017)

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  • Buijs, U.Universidad de Málaga
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  • Carrasquel Vera, Jose GabrielUCLouvain
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  • Murillo, A.Universidad de Málaga
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Abstract
In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers (a, b, c) (a,b,c) with a + b + c = n-1 a+b+c=n-1, n ≥ 4 n4. These identities are deduced by translating into homotopical terms the gauge action on the Maurer-Cartan set of a differential graded Lie algebra. We show that Euler and Miki's identities, well-known and apparently non-related formulas, are linear combinations of our family and they satisfy a particular symmetry relation.
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Buijs, U., Carrasquel Vera, J. G., & Murillo, A. (2017). The gauge action, DG Lie algebras and identities for Bernoulli numbers. Forum mathematicum, 29(2), 277-286. https://doi.org/10.1515/forum-2015-0257 (Original work published 2017)