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Greg Muller

  1. Skein algebras and cluster algebras of marked surfaces.

    Tue, 04/03/2012 - 15:01 — SomNambul
    Authors: Greg Muller
    Subjects: Quantum Algebra
    Abstract

    This paper defines several algebras associated to an oriented surface S with
    a finite set of marked points on the boundary. The first is the skein algebra
    Sk_q(S), which is spanned by links in the surface which are allowed to have
    endpoints at the marked points, modulo several locally defined relations. The
    product is given by superposition of links. A basis of this algebra is given,
    as well as several algebraic results.

  2. The Beilinson Equivalence for Differential Operators and Lie Algebroids.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: Greg Muller
    Subjects: Quantum Algebra
    Abstract

    Let D be the ring of differential operators on a smooth irreducible affine
    variety X over the complex numbers; or, more generally, the enveloping algebra
    of any locally free Lie algebroid on X. The category of finitely-generated
    graded modules of the Rees algebra D~ has a natural quotient category qgr(D~)
    which imitates the category of modules on Proj of a graded commutative ring. We
    show that the derived category D^b(qgr(D~)) is equivalent to the derived
    category of finitely-generated modules of a sheaf of algebras E on X which is
    coherent over X.

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