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Yael Fregier

  1. L-infinity algebras governing simultaneous deformations via derived brackets.

    Wed, 02/15/2012 - 15:01 — SomNambul
    Authors: Yael Fregier, Marco Zambon
    Subjects: Quantum Algebra
    Abstract

    We consider the problem of deforming simultaneously a pair of given
    structures. We show that such deformations are governed by an L-infinity
    algebra, which we construct explicitly. Our machinery is based on Th. Voronov's
    derived bracket construction.

    We consider algebraic and geometric applications, including the deformations
    of morphisms of various kinds of algebras, of coisotropic submanifolds in
    Poisson manifolds, and of twisted Poisson structures.

  2. On Hopf 2-algebras.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: Yael Fregier, Friedrich Wagemann
    Subjects: Group Theory
    Abstract

    Our main goal in this paper is to translate the diagram relating groups,

    Lie algebras and Hopf algebras to the corresponding 2-objects, i.e. to
    categorify it. This is done interpreting 2-objects as crossed modules and
    showing the compatibility of the standard functors linking groups, Lie algebras
    and Hopf algebras with the concept of a crossed module. One outcome is the
    construction of an enveloping algebra of the string Lie algebra of Baez-Crans,
    another is the clarification of the passage from crossed modules of Hopf
    algebras to Hopf 2-algebras.

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