Quantizing deformation theory II

2018/06/28 by Voronov, Alexander A.
#16E45 #18G55 (Primary) 14M30 #58A50 #81S22 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1806.11197

Abstract

A quantization of classical deformation theory, based on the Maurer-Cartan Equation dS + (1)/(2)[S,S] = 0 in dg-Lie algebras, a theory based on the Quantum Master Equation dS + ℏ ΔS + (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.

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