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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 719–737 (Mi mz8536)  

This article is cited in 1 scientific paper (total in 1 paper)

Extension of the Multiplication Operation in $E_\infty$-Algebras to an $A_\infty$-Morphism of $E_\infty$-Algebras and Cartan Objects in the Category of May Algebras

S. V. Lapin

Mordovian State Pedagogical Institute

Abstract: It is proved in the paper that the multiplication operation on an arbitrary $E_\infty$-algebra can be extended to an $E_\infty$-algebra $A_\infty$-morphism. As a corollary, it is proved that every May algebra defined by an $E_\infty$-algebra is a Cartan object in the category of May algebras.

Keywords: $E_\infty$-algebra, $A_\infty$-morphism, Cartan object, May algebra, differential module, Steenrod operations, cohomology of a topological space

DOI: https://doi.org/10.4213/mzm8536

Full text: PDF file (506 kB)
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English version:
Mathematical Notes, 2011, 89:5, 672–688

Bibliographic databases:

UDC: 515.14
Received: 11.10.2009
Revised: 09.06.2010

Citation: S. V. Lapin, “Extension of the Multiplication Operation in $E_\infty$-Algebras to an $A_\infty$-Morphism of $E_\infty$-Algebras and Cartan Objects in the Category of May Algebras”, Mat. Zametki, 89:5 (2011), 719–737; Math. Notes, 89:5 (2011), 672–688

Citation in format AMSBIB
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\by S.~V.~Lapin
\paper Extension of the Multiplication Operation in~$E_\infty$-Algebras to an $A_\infty$-Morphism of $E_\infty$-Algebras and Cartan Objects in the Category of May Algebras
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 5
\pages 719--737
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\crossref{https://doi.org/10.4213/mzm8536}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858560}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 5
\pages 672--688
\crossref{https://doi.org/10.1134/S0001434611050087}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Lapin, “Chain Realization of Differential Modules with $\infty$-Simplicial Faces and the $B$-Construction over $A_\infty$-Algebras”, Math. Notes, 98:1 (2015), 111–129  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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