Geodesic
Brave new Hopf algebroids and extensions of $MU$-algebras
Homology, homotopy, and applications, Tome 4 (2002) no. 1, pp. 163-173.

Voir la notice de l'article provenant de la source International Press of Boston

We apply recent work of A. Lazarev which develops an obstruction theory for the existence of $R$-algebra structures on $R$-modules, where $R$ is a commutative $S$-algebra. We show that certain $MU$-modules have such $A_\infty$ structures. Our results are often simpler to state for the related $BP$-modules under the currently unproved assumption that $BP$ is a commutative $S$-algebra. Part of our motivation is to clarify the algebra involved in Lazarev’s work and to generalize it to other important cases. We also make explicit the fact that $BP$ admits an $MU$-algebra structure as do $E(n)$ and $\widehat{E(n)}$, in the latter case rederiving and strengthening older results of U. Würgler and the first author.
DOI : 10.4310/HHA.2002.v4.n1.a9
Classification : 55N20, 55N45, 55P43, 55S35, 55T25
Keywords: $R$-algebra, Hopf algebroid, obstruction theory 
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     title = {Brave new {Hopf} algebroids and extensions of $MU$-algebras},
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Andrew Baker; Alain Jeanneret. Brave new Hopf algebroids and extensions of $MU$-algebras. Homology, homotopy, and applications, Tome 4 (2002) no. 1, pp. 163-173. doi : 10.4310/HHA.2002.v4.n1.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2002.v4.n1.a9/

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