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Xiang Tang

  1. Hochschild (co)homology of the Dunkl operator quantization of $\Z_2$-singularity.

    Втр, 10/26/2010 - 15:01 — SomNambul
    Authors: Xiang Tang, Ajay Ramadoss
    Subjects: Quantum Algebra
    Abstract

    We study Hochschild (co)homology groups of the Dunkl operator quantization of
    $\Z_2$-singularity constructed by Halbout and Tang. Further, we study traces on
    this algebra and prove a local algebraic index formula.

  2. Hopf cyclic cohomology and Hodge theory for proper actions.

    Ср, 02/24/2010 - 16:01 — SomNambul
    Authors: Weiping Zhang, Xiang Tang, Yi-jun Yao
    Subjects: Differential Geometry
    Abstract

    We introduce a Hopf algebroid associated to a proper Lie group action on a
    smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is
    equal to the de Rham cohomology of invariant differential forms. When the
    action is cocompact, we develop a generalized Hodge theory for the de Rham
    cohomology of invariant differential forms. We prove that every cyclic
    cohomology class of the Hopf algebroid is represented by a generalized harmonic
    form. This implies that the space of cyclic cohomology of the Hopf algebroid is
    finite dimensional.

  3. A Survey on Rankin-Cohen Deformations.

    Сб, 09/26/2009 - 04:10 — SomNambul
    Authors: Xiang Tang, Richard Rochberg, Yi-jun Yao
    Subjects: Quantum Algebra
    Abstract

    This is a survey about recent progress in Rankin-Cohen deformations. We
    explain a connection between Rankin-Cohen brackets and higher order Hankel
    forms.

  4. Dunkl operator and quantization of $\mathbb{Z}_2$-singularity.

    Втр, 09/01/2009 - 12:47 — SomNambul
    Authors: Gilles Halbout, Xiang Tang
    Subjects: Quantum Algebra
    Abstract

    Let $(X,\omega)$ be a symplectic orbifold which is locally like the quotient
    of a $\mathbb{Z}_2$ action on $\reals^n$. Let $A^{((\hbar))}_X$ be a
    deformation quantization of $X$ constructed via the standard Fedosov method
    with characteristic class being $\omega$. In this paper, we construct a
    universal deformation of the algebra $A^{((\hbar))}_X$ parametrized by
    codimension 2 components of the associated inertia orbifold $\widetilde{X}$.
    This partially confirms a conjecture of Dolgushev and Etingof in the case of
    $\mathbb{Z}_2$ orbifolds.

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