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arXiv · 2512.04780

Tensorial Permanence of $K$-Stability for Diagonal AH-Algebras

Apurva Seth
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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.

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Apurva Seth. 2025-12-04. Tensorial Permanence of $K$-Stability for Diagonal AH-Algebras. https://doi.org/10.1112/blms.70398

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