Hopf algebras of diagrams
Combinatorics
2007-10-31 v1
Abstract
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these algebras are indexed either by bipartite graphs (labelled or unlabbeled) or by packed matrices (with integer or set coefficients). Realizations on biword are exhibited, and it is shown how these algebras fit into a commutative diagram. Hopf deformations and dendriform structures are also considered for some algebras in the picture.
Keywords
Cite
@article{arxiv.0710.5661,
title = {Hopf algebras of diagrams},
author = {Gerard Henry Edmond Duchamp and Jean-Gabriel Luque and Jean-Christophe Novelli and Christophe Tollu and Frederic Toumazet},
journal= {arXiv preprint arXiv:0710.5661},
year = {2007}
}
Comments
21 pages, LaTEX