Quantizing deformation theory

John Terilla

A chapter in Deformation Spaces, 2010, pp 135-141 from Springer

Abstract: Abstract We describe a step toward quantizing deformation theory. The L ∞ operad is encoded in a Hochschild cocyle o1 in a simple universal algebra (P, o0). This Hochschild cocyle can be extended naturally to a star product ‚=o0+ħo1+ħ2o2 +…. The algebraic structure encoded in * is the properad Ω(coFrob) which, conjecturally, controls a quantization of deformation theory—a theory for which Frobenius algebras replace ordinary commutative parameter rings.

Keywords: Complex Manifold; Associative Algebra; Deformation Theory; String Topology; Parameter Ring (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-8348-9680-3_6

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