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

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

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English version:
Mathematical Notes, 2011, 89:5, 672–688

Bibliographic databases:

UDC: 515.14
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
\Bibitem{Lap11} \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 \mathnet{http://mi.mathnet.ru/mz8536} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000292216000008} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959675855} 

• http://mi.mathnet.ru/eng/mz8536
• https://doi.org/10.4213/mzm8536
• http://mi.mathnet.ru/eng/mz/v89/i5/p719

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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