Asymptotically split extensions and E-theory

一类渐近阿贝尔C*-代数的McMillan定理

The McMillan theorem for a class of asymptotically abelian C*-algebras

该研究将Shannon-McMillan-Breiman定理拓展到一类渐近阿贝尔C*-代数对应的非交换动力系统中，推广了经典定理的适用范围。

Split extensions and KK-equivalences for quantum projective spaces

We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the commutative algebra $\mathbb{C}^{n+1}$. Our construction relies on showing that the extension of $C^*$-algebras relating two quantum projective spaces of successive dimensions admits a splitting, which we can describe explicitly using graph algebra techniques.

Complete descriptions of intermediate operator algebras by intermediate extensions of dynamical systems

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely describe all intermediate operator algebras: the Galois Correspondence Theorem and the Tensor Splitting Theorem. Here we establish the third, new complete description theorem which gives a canonical bijective correspondence between intermediate operator algebras and intermediate extensions of dynamical systems. One can also regard this theorem as a crossed pro…