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Li Guo

  1. PostLie algebra structures on the Lie algebra sl(2,C).

    Tue, 11/29/2011 - 15:01 — SomNambul
    Authors: Chengming Bai, Li Guo, Yu Pan, Qing Liu
    Subjects: Rings and Algebras
    Abstract

    The PostLie algebra is an enriched structure of the Lie algebra that has
    recently arisen from operadic study. It is closely related to pre-Lie algebra,
    Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter
    equations and integrable systems. We give a complete classification of PostLie
    algebra structures on the Lie algebra sl(2,C) up to isomorphism. We first
    reduce the classification problem to solving an equation of 3 x 3 matrices.

  2. Splitting of operations, Manin products and Rota-Baxter operators.

    Fri, 07/01/2011 - 15:01 — SomNambul
    Authors: Chengming Bai, Xiang Ni, Li Guo, Olivia Bellier
    Subjects: Quantum Algebra
    Abstract

    This paper provides a general operadic definition for the notion of splitting
    the operations of algebraic structures. This construction is proved to be
    equivalent to some Manin products of operads and it is shown to be closely
    related to Rota-Baxter operators. Hence, it gives a new effective way to
    compute Manin black products. The present construction is shown to have
    symmetry properties.

  3. O-operators on associative algebras and dendriform algebras.

    Mon, 03/15/2010 - 16:01 — SomNambul
    Authors: Chengming Bai, Xiang Ni, Li Guo
    Subjects: Rings and Algebras
    Abstract

    We generalize the well-known construction of dendriform dialgebras and
    trialgebras from Rota-Baxter algebras to a construction from O-operators. We
    then show that this construction from O-operators gives all dendriform
    dialgebras and trialgebras. Furthermore there are bijections between certain
    equivalence classes of invertible O-operators and certain equivalence classes
    of dendriform dialgebras and trialgebras.

  4. Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras.

    Tue, 10/20/2009 - 12:53 — SomNambul
    Authors: Chengming Bai, Xiang Ni, Li Guo
    Subjects: Mathematical Physics
    Abstract

    We generalize the classical study of (generalized) Lax pairs and the related
    $O$-operators and the (modified) classical Yang-Baxter equation by introducing
    the concepts of nonabelian generalized Lax pairs, extended $\calo$-operators
    and the extended classical Yang-Baxter equation. We study in this context the
    nonabelian generalized $r$-matrix ansatz and the related double Lie algebra
    structures. Relationship between extended $O$-operators and the extended
    classical Yang-Baxter equation is established, especially for self-dual Lie
    algebras.

  5. $O$-operators on associative algebras and associative Yang-Baxter equations.

    Tue, 10/20/2009 - 12:53 — SomNambul
    Authors: Chengming Bai, Xiang Ni, Li Guo
    Subjects: Rings and Algebras
    Abstract

    We introduce the concept of an extended O-operator that generalizes the
    well-known concept of a Rota-Baxter operator. We study the associative products
    coming from these operators and establish the relationship between extended
    O-operators and the associative Yang-Baxter equation, extended associative
    Yang-Baxter equation and generalized Yang-Baxter equation.

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