Compatibility of the Feigin-Frenkel Isomorphism and the Harish-Chandra Isomorphism for jet algebras

THE HARISH-CHANDRA ISOMORPHISM FOR sl(2,C)

Given a reductive Lie algebra g and choice of Cartan subalgebra h, the HarishChandra map gives an isomorphism between the center z of the universal enveloping algebra U(g) of g and the algebra of Weyl group invariant symmetric tensors of h, denoted S(h) . We define these objects and give a sketch of the proof, using sl(2,C) as a motivating example. The proofs and examples mirror those found in ...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Jet Isomorphism for Conformal Geometry

Local invariants of a metric in Riemannian geometry are quantities expressible in local coordinates in terms of the metric and its derivatives and which have an invariance property under changes of coordinates. It is a fundamental fact that such invariants may be written in terms of the curvature tensor of the metric and its covariant derivatives. In this form, they can be identified with invar...

The Isomorphism Relation for Separable C*-algebras

We prove that the isomorphism relation for separable C∗-algebras, and also the relations of complete and n-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.

The Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras

Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.