The Isomorphism of Hall Algebras

On Isomorphism of Simplicial Complexes and Their Related Algebras

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

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.

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.

Lectures on Hall Algebras

These notes represent the written, expanded and improved version of a series of lectures given at the winter school “Representation theory and related topics” held at the ICTP in Trieste in January 2006. The topic for the lectures was “Hall algebras” and I have tried to give a survey of what I believe are the most fundamental results and examples in this area. The material was divided into five...