Abstract:We study $K$-stability for tensor products of diagonal AH-algebras with arbitrary C*-algebras. Our main result provides a characterization of $K$-stability: for a diagonal AH-algebra $A = \varinjlim (A_i, \varphi_i)$, $A \otimes B$ is $K$-stable for every C*-algebra $B$ if and only if the sizes of the matrix blocks in the inductive system grow without bound. As applications, we show that non-$\mathcal{Z}$-stable Villadsen algebras of the first kind are $K$-stable when tensored with any C*-algebra. Moreover, any simple, unital, infinite-dimensional diagonal AH-algebra automatically satisfies this growth condition, and therefore its tensor product with arbitrary C*-algebras is always $K$-stable.
From: Apurva Seth [view email]
[v1]
Thu, 4 Dec 2025 13:25:59 UTC (19 KB)
[v2]
Fri, 22 May 2026 16:00:56 UTC (24 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。