This article is cited 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.

UDC: 515.14

Received: 11.10.2009
Revised: 09.06.2010

DOI: 10.4213/mzm8536

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

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