$K$-Stability of A$\mathbb{T}$-Algebras

TL;DR

This paper presents a method to compute the rational nonstable K-groups of A$ ext{T}$-algebras and establishes a link between K-stability and slow dimension growth.

Contribution

It introduces a procedure for calculating K-groups of A$ ext{T}$-algebras and characterizes K-stability in terms of slow dimension growth.

Findings

Rational nonstable K-groups of A$ ext{T}$-algebras can be computed explicitly.

K-stability of A$ ext{T}$-algebras is equivalent to having slow dimension growth.

Abstract

We describe a procedure to compute the rational nonstable K-groups of A$\mathbb{T}$-algebras. As an application, we show that an A$\mathbb{T}$-algebra is K-stable if and only if it has slow dimension growth.