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

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Matematicheskie Zametki, 2011, Volume 89, Issue 5, Pages 719–737
DOI: https://doi.org/10.4213/mzm8536 (Mi mzm8536)

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

Extension of the Multiplication Operation in

E_{\infty}

$E_\infty$ -Algebras to an

A_{\infty}

$A_\infty$ -Morphism of

E_{\infty}

$E_\infty$ -Algebras and Cartan Objects in the Category of May Algebras

S. V. Lapin

Mordovian State Pedagogical Institute

Full-text PDF (506 kB) Citations (1)

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

Abstract: It is proved in the paper that the multiplication operation on an arbitrary

E_{\infty}

$E_\infty$ -algebra can be extended to an

E_{\infty}

$E_\infty$ -algebra

A_{\infty}

$A_\infty$ -morphism. As a corollary, it is proved that every May algebra defined by an

E_{\infty}

$E_\infty$ -algebra is a Cartan object in the category of May algebras.

Keywords:

E_{\infty}

$E_\infty$ -algebra,

A_{\infty}

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

Received: 11.10.2009
Revised: 09.06.2010

English version:
Mathematical Notes, 2011, Volume 89, Issue 5, Pages 672–688
DOI: https://doi.org/10.1134/S0001434611050087

Bibliographic databases:

Document Type: Article

UDC: 515.14

Language: Russian

Citation: S. V. Lapin, “Extension of the Multiplication Operation in

E_{\infty}

$E_\infty$ -Algebras to an

A_{\infty}

$A_\infty$ -Morphism of

E_{\infty}

$E_\infty$ -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/mzm8536}

\crossref{https://doi.org/10.4213/mzm8536}

\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000292216000008}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959675855}

Linking options:

https://www.mathnet.ru/eng/mzm8536

https://doi.org/10.4213/mzm8536

https://www.mathnet.ru/eng/mzm/v89/i5/p719

This publication is cited in the following 1 articles:

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

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

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Abstract page:	4385
Full-text PDF :	975
References:	116
First page:	307

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