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Donald Yau

  1. Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras.

    Втр, 02/23/2010 - 16:01 — SomNambul
    Authors: Donald Yau
    Subjects: Rings and Algebras
    Abstract

    Hom-Maltsev(-admissible) algebras are defined, and it is shown that
    Hom-alternative algebras are Hom-Maltsev-admissible. With a new definition of a
    Hom-Jordan algebra, it is shown that Hom-alternative algebras are
    Hom-Jordan-admissible. Hom-type generalizations of some well-known identities
    in alternative algebras, including the Moufang identities, are obtained.

  2. Infinitesimal Hom-bialgebras and Hom-Lie bialgebras.

    Чт, 01/28/2010 - 16:01 — SomNambul
    Authors: Donald Yau
    Subjects: Rings and Algebras
    Abstract

    We study the Hom-type generalization of infinitesimal bialgebras, called
    infinitesimal Hom-bialgebras. In particular, we consider infinitesimal
    Hom-bialgebras arising from quivers, the sub-classes of coboundary and
    quasi-triangular infinitesimal Hom-bialgebras, the associative Hom-Yang-Baxter
    equation, and homological perturbation of the comultiplications in
    infinitesimal Hom-bialgebras. The relationships between infinitesimal
    Hom-bialgebras, Hom-Lie bialgebras, and the classical Hom-Yang-Baxter equation
    are also studied.

  3. Hom-quantum groups III: Representations and module Hom-algebras.

    Втр, 12/01/2009 - 16:01 — SomNambul
    Authors: Donald Yau
    Subjects: Quantum Algebra
    Abstract

    We study Hom-quantum groups, their representations, and module Hom-algebras.
    Two Twisting Principles for Hom-type algebras are formulated, and construction
    results are proved following these Twisting Principles. Examples include
    Hom-quantum n-spaces, Hom-quantum enveloping algebras of Kac-Moody algebras,
    Hom-Verma modules, and Hom-type analogs of U_q(sl_2)-module-algebra structures
    on the quantum planes.

  4. On homotopy invariance for algebras over colored PROPs.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Donald Yau, Mark W. Johnson
    Subjects: Algebraic Topology
    Abstract

    Over a monoidal model category, under some mild assumptions, we equip the
    categories of colored PROPs and their algebras with projective model category
    structures. A Boardman-Vogt style homotopy invariance result about algebras
    over cofibrant colored PROPs is proved. As an example, we define homotopy
    topological conformal field theories and observe that such structures are
    homotopy invariant.

  5. On homotopy invariance for algebras over colored PROPs.

    Пт, 09/18/2009 - 11:36 — SomNambul
    Authors: Donald Yau, Mark W. Johnson
    Subjects: Algebraic Topology
    Abstract

    Over a monoidal model category, under some mild assumptions, we equip the
    categories of colored PROPs and their algebras with projective model category
    structures. A Boardman-Vogt style homotopy invariance result about algebras
    over cofibrant colored PROPs is proved. As an example, we define homotopy
    topological conformal field theories and observe that such structures are
    homotopy invariant.

  6. Hom-Novikov algebras.

    Пт, 09/04/2009 - 12:10 — SomNambul
    Authors: Donald Yau
    Subjects: Rings and Algebras
    Abstract

    We study a twisted generalization of Novikov algebras, called Hom-Novikov
    algebras, in which the two defining identities are twisted by a linear map. It
    is shown that Hom-Novikov algebras can be obtained from Novikov algebras by
    twisting along any algebra endomorphism. All algebra endomorphisms on complex
    Novikov algebras of dimensions two or three are computed, and their associated
    Hom-Novikov algebras are described explicitly.

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