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

  • Urtzi Buijs , José G. Carrasquel-Vera and Aniceto Murillo EMAIL logo
Published/Copyright: June 8, 2017
Forum Mathematicum
From the journal Forum Mathematicum Volume 29 Issue 2

Abstract

In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers (a,b,c) with a+b+c=n-1, n≥4. 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.

Keywords: Gauge action; Bernoulli numbers; homotopy theory of Lie algebras
MSC 2010: 17B01; 11B68; 55U35

Communicated by Frederick R. Cohen

Funding source: Ministerio de Economía y Competitividad

Award Identifier / Grant number: MTM2010-15831

Award Identifier / Grant number: MTM2013-41768-P

Award Identifier / Grant number: FQM-213

Award Identifier / Grant number: MTM2010-18089

Award Identifier / Grant number: MTM2013-41768-P

Funding statement: The first author was partially supported by the Ministerio de Economía y Competitividad grants MTM2010-15831, MTM2013-41768-P, by the grants FQM-213, and by the Marie Curie COFUND programme U-mobility, co-financed by the University of Málaga, the European Commision FP7 under GA No. 246550, and Ministerio de Economía y Competitividad (COFUND2013-40259). The second author was partially supported by the Ministerio de Economía y Competitividad grant MTM2010-18089. The third author was partially supported by the Ministerio de Economía y Competitividad grant MTM2013-41768-P and by the Junta de Andalucía grants FQM-213.

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Received: 2015-12-21
Revised: 2016-3-25
Published Online: 2017-6-8
Published in Print: 2017-3-1

© 2017 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. A note on the Hilali conjecture
  3. Finite groups have more conjugacy classes
  4. The gauge action, DG Lie algebras and identities for Bernoulli numbers
  5. Unitary embeddings of finite loop spaces
  6. Topological complexity of planar polygon spaces with small genetic code
  7. Numerical semigroups in a problem about cost-effective transport
  8. On the smallest simultaneous power nonresidue modulo a prime
  9. Decompositions of the higher order polars of plane branches
  10. A formula for the expected volume of the Wiener sausage with constant drift
  11. The slice spectral sequence for the C4 analog of real K-theory
  12. Incidences between points and generalized spheres over finite fields and related problems
  13. Mean values of the Witten L-function for SU(2)
  14. A direct computation of the cohomology of the braces operad
  15. Abelian varieties over finite fields as basic abelian varieties
https://doi.org/10.1515/forum-2015-0257
Keywords for this article
Gauge action; Bernoulli numbers; homotopy theory of Lie algebras

Articles in the same Issue

  1. Frontmatter
  2. A note on the Hilali conjecture
  3. Finite groups have more conjugacy classes
  4. The gauge action, DG Lie algebras and identities for Bernoulli numbers
  5. Unitary embeddings of finite loop spaces
  6. Topological complexity of planar polygon spaces with small genetic code
  7. Numerical semigroups in a problem about cost-effective transport
  8. On the smallest simultaneous power nonresidue modulo a prime
  9. Decompositions of the higher order polars of plane branches
  10. A formula for the expected volume of the Wiener sausage with constant drift
  11. The slice spectral sequence for the C4 analog of real K-theory
  12. Incidences between points and generalized spheres over finite fields and related problems
  13. Mean values of the Witten L-function for SU(2)
  14. A direct computation of the cohomology of the braces operad
  15. Abelian varieties over finite fields as basic abelian varieties
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