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Hochschild cohomology and moduli spaces of strongly homotopy associative algebras. (English) Zbl 1032.16008

Author’s abstract: Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of invertible power series acting on a certain space. The Hochschild cohomology rings of resulting \(A_\infty\)-algebras have an interpretation as totally ramified extensions of discrete valuation rings. All \(A_\infty\)-algebras are supposed to be unital and we give a detailed analysis of unital structures which is of independent interest.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16E45 Differential graded algebras and applications (associative algebraic aspects)
14J10 Families, moduli, classification: algebraic theory
13F25 Formal power series rings
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