From Dixmier Algebras to Star Products

Dixmier Approximation and Symmetric Amenability for C ∗ - Algebras

We study some general properties of tracial C∗-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C∗-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.

Titles and Abstracts for the Algebra Extravaganza

Title: The Dixmier-Moeglin equivalence for D-groups Abstract: The Dixmier-Moeglin equivalence is a characterization of the primitive ideals of an algebra that holds for many classes of rings, including affine PI rings, enveloping algebras of finite-dimensional Lie algebras, and many quantum algebras. For rings satisfying this equivalence, it says that the primitive ideals are precisely those pr...

Poisson Algebras via Model Theory and Differential-algebraic Geometry

Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is sho...

Quantization of Nilpotent Coadjoint Orbits Quantization of Nilpotent Coadjoint Orbits Quantization of Nilpotent Coadjoint Orbits

Let G be a complex reductive group. We study the problem of associating Dixmier algebras to nilpotent (co)adjoint orbits of G, or, more generally, to orbit data for G. If g = 0 + n + in is a triangular decomposition of g and 0 is a nilpotent orbit, we consider the irreducible components of 0 n n, which are Lagrangian subvarieties of 0. The main idea is to construct, starting with certain "good"...

Connected Hopf Algebras with Dixmier Basis and Infinite Primary Decomposition