Tensorial Permanence of K-Stability for Diagonal AH-Algebras

2025/12/04 by Seth, Apurva
#46L85 (Primary) 46L80 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2512.04780

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, φ_i), A ⊗ 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-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.

Citations

• A class of simple C*-algebras with stable rank one
• On the classification problem for nuclear C*-algebras
• Nonstable K-theory for Z-stable C*-algebras

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