## 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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