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Matthew Szczesny

  1. Colored trees and noncommutative symmetric functions.

    Втр, 09/22/2009 - 14:09 — SomNambul
    Authors: Matthew Szczesny
    Subjects: Quantum Algebra
    Abstract

    Let $\CRF_S$ denote the category of $S$-colored rooted forests, and
    $\H_{\CRF_S}$ denote its Ringel-Hall algebra as introduced in \cite{KS}. We
    construct a homomorphism from a $K^+_0 (\CRF_S)$--graded version of the Hopf
    algebra of noncommutative symmetric functions to $\H_{\CRF_S}$. Dualizing, we
    obtain a homomorphism from the Connes-Kreimer Hopf algebra to a $K^+_0
    (\CRF_S)$--graded version of the algebra of quasisymmetric functions. This
    homomorphism is a refinement of one considered by W. Zhao in \cite{Z}.

  2. Rooted trees, Feynman graphs, and Hecke correspondences.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Matthew Szczesny
    Subjects: Quantum Algebra
    Abstract

    We construct natural representations of the Connes-Kreimer Lie algebras on
    rooted trees/Feynman graphs arising from Hecke correspondences in the
    categories $\LRF, \LFG$ constructed by K. Kremnizer and the author. We thus
    obtain the insertion/elimination representations constructed by Connes-Kreimer
    as well as an isomorphic pair we term top-insertion/top-elimination. We also
    construct graded finite-dimensional sub/quotient representations of these
    arising from "truncated" correspondences.

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