Geodesic
Commutative $A_\infty$-algebras and the functor~$\mathscr D$
Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1557-1571

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We consider the question of calculating the set of equivalence classes of commutative $A_\infty$-algebras and the connection between this question and calculating the functor $\mathscr D$ introduced by Berikashvili. In particular, we show that there are no non-trivial commutative $A_\infty$-structures on a free commutative algebra. 
@article{SM_2002_193_10_a7,
     author = {S. A. Yakshin},
     title = {Commutative $A_\infty$-algebras and the functor~$\mathscr D$},
     journal = {Sbornik. Mathematics},
     pages = {1557--1571},
     publisher = {mathdoc},
     volume = {193},
     number = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_10_a7/}
}
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S. A. Yakshin. Commutative $A_\infty$-algebras and the functor~$\mathscr D$. Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1557-1571. http://geodesic.mathdoc.fr/item/SM_2002_193_10_a7/