RECURSIVELY GENERATING FORMALITY QUASI-ISOMORPHISMS WITH APPLICATIONS TO DEFORMATION QUANTIZATION

Abstract

Formality quasi-isomorphisms Cobar(C) -> O are a necessary component of the machinery used in deformation quantization to produce quantized algebras of observables, however they are often constructed via transcendental methods, resulting in computational difficulties and quasi-isomorphisms defined over extensions of Q We will show that these formality quasi-isomorphisms can be "demystified" for a large class of dg-operads, by showing that they can be constructed recursively via an algorithm that builds them from systems of linear equations over Q, given certain assumptions on H(O).