Homological dimensions of smooth and complex analytic quantum tori

解析泛函代数与同调满同态

Algebras of analytic functionals and homological epimorphisms

本文证明连通复李群上的解析泛函代数在无需可解性假设下满足同调满同态性质，并推广到更一般的完备化同态，包括关于Banach PI-代数的包络。

解析泛函代数及其完备化的同调维数

Homological dimensions of algebras of analytic functionals and their completions

本文证明连通复李群上解析泛函代数及其某些完备化的主要同调维数等于该群线性化典范分解中单连通可解因子的维数，线性复约化因子不影响这些代数的同调性质。

Homological dimensions of analytic Ore extensions

If $A$ is an algebra with finite right global dimension, then for any automorphism $α$ and $α$-derivation $δ$ the right global dimension of $A[t; α, δ]$ satisfies \[ \text{rgld} \, A \le \text{rgld} \, A[t; α, δ] \le \text{rgld} \, A + 1. \] We extend this result to the case of holomorphic Ore extensions and smooth crossed products by $\mathbb{Z}$ of $\hat{\otimes}$-algebras.

非交换复解析几何的同调框架与函数演算

Homological framework of noncommutative complex analytic geometry and functional calculus

本文提出非交换复解析几何的同调框架，解决函数演算问题，并将相关谱简化为Putinar谱或泰勒谱。