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Pseudo Maurer–Cartan perturbation algebra and pseudo perturbation lemma

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Published/Copyright: April 6, 2019
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 26 Issue 2

Abstract

We introduce the pseudo Maurer–Cartan perturbation algebra, establish a structural result and explore the structure of this algebra. That structural result entails, as a consequence, what we refer to as the pseudo perturbation lemma. This lemma, in turn, implies the ordinary perturbation lemma.

Keywords: homological perturbation theory; deformation theory; abstract gauge theory; pseudo Maurer–Cartan perturbation algebra; pseudo perturbation lemma
MSC 2010: 16E45; 17B55; 18G35; 18G50; 18G55; 55R20; 55U15

Dedicated to Nodar Berikashvili

Funding source: Labex

Award Identifier / Grant number: ANR-11-LABX-0007-01

Funding statement: I gratefully acknowledge support by the CNRS and by the Labex CEMPI (ANR-11-LABX-0007-01).

Acknowledgements

I am indebted to Jim Stasheff for a number of most valuable comments on a draft of the paper.

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Received: 2018-10-03
Accepted: 2018-12-12
Published Online: 2019-04-06
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On formal group laws over the quotients of Lazard’s ring
  3. Finite spaces and an axiomatization of the Lefschetz number
  4. Action theory of alternative algebras
  5. Pseudo Maurer–Cartan perturbation algebra and pseudo perturbation lemma
  6. Homotopy classification of morphisms of differential graded algebras
  7. Distance between the spectra of graphs with respect to normalized Laplacian spectra
  8. Multi-dimensional periodic problems for higher-order linear hyperbolic equations
  9. Dihedral ∞-simplicial modules and dihedral homology of involutive homotopy unital A∞-algebras
  10. Polynomial solutions to linear PDEs with constant coefficients
  11. On Küneth’s correlation and its applications
  12. On the construction of a covering map
  13. L∞ in physics and in Georgia
  14. An example of a hereditarily normal topologically finite space, which is topologically infinite relative to the class of all its proper Fσ-subspaces
https://doi.org/10.1515/gmj-2019-2020
Keywords for this article
homological perturbation theory; deformation theory; abstract gauge theory; pseudo Maurer–Cartan perturbation algebra; pseudo perturbation lemma

Articles in the same Issue

  1. Frontmatter
  2. On formal group laws over the quotients of Lazard’s ring
  3. Finite spaces and an axiomatization of the Lefschetz number
  4. Action theory of alternative algebras
  5. Pseudo Maurer–Cartan perturbation algebra and pseudo perturbation lemma
  6. Homotopy classification of morphisms of differential graded algebras
  7. Distance between the spectra of graphs with respect to normalized Laplacian spectra
  8. Multi-dimensional periodic problems for higher-order linear hyperbolic equations
  9. Dihedral ∞-simplicial modules and dihedral homology of involutive homotopy unital A∞-algebras
  10. Polynomial solutions to linear PDEs with constant coefficients
  11. On Küneth’s correlation and its applications
  12. On the construction of a covering map
  13. L∞ in physics and in Georgia
  14. An example of a hereditarily normal topologically finite space, which is topologically infinite relative to the class of all its proper Fσ-subspaces
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