2008/07/11 by Walid Aloulou, Aloulou, Walid
Mathematics · #16E45 #16W30 #17B63 #18G55 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16E45 #msc:16W30 #msc:17B63 #msc:18G55
paper · pdf · doi:10.48550/arxiv.0807.1853
arxiv created 2008/07/11 · arxiv updated 2009/12/01
We study in this article the concepts of algebra up to homotopy for a structure defined by two operations \pt and [, ]. Having determined the structure of G_∞ algebras and P_∞ algebras, we generalize this construction and we define a structure of (a, b)-algebra up to homotopy. Given a structure of commutative and differential graded Lie algebra for two shifts degree given by a and b, we will give an explicit construction of the associate algebra up to homotopy