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Quantizing deformation theory

In: Deformation Spaces

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  • John Terilla

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.

Suggested Citation

  • John Terilla, 2010. "Quantizing deformation theory," Springer Books, in: Hossein Abbaspour & Matilde Marcolli & Thomas Tradler (ed.), Deformation Spaces, pages 135-141, Springer.
    • Handle: RePEc:spr:sprchp:978-3-8348-9680-3_6
    DOI: 10.1007/978-3-8348-9680-3_6
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