Quantizing deformation theory II

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A quantization of classical deformation theory, based on the Maurer-Cartan Equation dS +12[S, S] = 0 in dg-Lie algebras, a theory based on the Quantum Master Equation dS +ħΔS + 1 2{S, S} = 0 in dg-BV-algebras, is proposed. Representability theorems for solutions of the Quantum Master Equation are proven. Examples of “quantum” deformations are presented.

Original languageEnglish (US)
Pages (from-to)125-152
Number of pages28
JournalPure and Applied Mathematics Quarterly
Issue number1
StatePublished - 2020

Bibliographical note

Funding Information:
Received June 21, 2018. 2010 Mathematics Subject Classification: Primary 14D15, 16E45; secondary 81T70. ∗The author is supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and a Collaboration grant from the Simons Foundation (#282349).

Publisher Copyright:
© 2020, International Press of Boston, Inc.. All rights reserved.


  • BV-algebra
  • Deformation theory
  • Differential graded manifold
  • Maurer-Cartan equation
  • Quantum Master Equation


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