2004/05/04 by Bruno Vallette, Vallette, Bruno · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0405057
Ph. D. Thesis (in french)
arxiv created 2004/05/04 · arxiv updated 2009/12/01
In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs. The operads are algebraic objects that represent the operations with multiple inputs but only one output acting on a certain type of algebras. A PROP models the operations with multiple inputs and multiple outputs acting on algebraic structures like bialgebras and Lie bialgebras. We also give a construction of the free monoid (for a monoidal product non-necessarily bilinear). We generalize the Poincare series of operads to PROPs and we prove a functional equation for Poincare series of Koszul PROPs.