2006/07/18 by Eduardo Hoefel, Hoefel, Eduardo · 3 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.math/0607435
OCHA is the homotopy algebra of open-closed strings. It can be defined as a sequence of multilinear operations on a pair of DG spaces satisfying certain relations which include the L_∞ relations in one space and the A_∞ relations in the other. In this paper we show that the OCHA structure is intrinsic to the tensor product of the symmetric and tensor coalgebras. We also show how an OCHA can be obtained from A_∞-extesions and define the \it universal enveloping A_∞-algebra of an OCHA as an A_∞-extension of the universal enveloping of its L_∞ part by its A_∞ part.