2017/03/15 by Joseph Chuang, Andrey Lazarev, Chuang, Joseph +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1703.05296
14 pages
arxiv created 2017/10/04 · arxiv updated 2017/10/05
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of the Homological Perturbation Lemma and its multiplicative version. As an application we give an explicit form of the decomposition theorem for A_∞ algebras and A_∞ modules and, more generally, for twisted objects in differential graded categories.