Hochschild cohomology and moduli spaces of strongly homotopy associative algebras

Details Hochschild cohomology and moduli spaces of strongly homotopy associative algebras Hochschild cohomology and moduli spaces of strongly homotopy associative algebras

2002-04-04

arxiv.org/abs/math/0204062v3

Mathematics

Quantum Algebra

Slightly expanded version. Minor inaccuracies and misprints corrected

Scientific paper

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-infinity algebras have an interpretation as totally ramified extensions of discrete valuation rings. All A-infinity algebras are supposed to be unital and we give a detailed analysis of unital structures which is of independent interest.

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