Commutative $A_\infty$-algebras and the functor $\mathscr D$

S. A. Yakshin

Moscow State Pedagogical University

Abstract: 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.

MSC: Primary 18G35; Secondary 55P40, 55P43, 55T05, 55U15

Received: 22.05.2001

DOI: 10.4213/sm689

 English version: Sbornik: Mathematics, 2002, 193:10, 1557–1571

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