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.


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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