Combinatorics and Formal Geometry of the Maurer–Cartan Equation

• DOI: 10.1007/s11005-012-0586-1
• Publication Date: 2012-10-09T17:31:45Z
• Authors: Joseph Chuang; Andrey Lazarev
• Keywords: High Energy Physics - Theory; FOS: Physical sciences; 01 natural sciences; 18D50, 17B55, 17B66, 16E45; High Energy Physics - Theory (hep-th); Mathematics - Quantum Algebra; FOS: Mathematics; Quantum Algebra (math.QA); Algebraic Topology (math.AT); Mathematics - Algebraic Topology; 0101 mathematics; QA

We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting is encoded in certain automorphisms of these universal objects.