On nuclear C∗-algebras

On the classification of nuclear C-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.

On the Classification Problem for Nuclear C-algebras

We exhibit a counterexample to Elliott’s classification conjecture for simple, separable, and nuclear C∗-algebras whose construction is elementary, and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves. The consequences for the program to class...

Decomposable Approximations of Nuclear C∗-algebras

We show that nuclear C∗-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C∗-algebra A which is closely contained in a C∗-algebra B embeds into B. The decomposition rank and nuclear dimension ...

Covering Dimension for Nuclear C * -algebras

We introduce the completely positive rank, a notion of covering dimension for nuclear C *-algebras and analyze some of its properties. The completely positive rank behaves nicely with respect to direct sums, quotients, ideals and inductive limits. For abelian C *-algebras it coincides with covering dimension of the spectrum and there are similar results for continuous trace algebras. As it turn...