The Classification Problem for Simple Unital Finite Rank Dimension Groups

TL;DR

This paper investigates how the complexity of classifying finite-rank unital simple dimension groups grows with rank, revealing increased difficulty in determining isomorphism as rank increases.

Contribution

It establishes that the Borel complexity of the isomorphism problem escalates with rank for these groups, impacting related classification problems.

Findings

Complexity increases with rank for isomorphism problems.

Implications for classification of Bratteli diagrams and LDA-groups.

Highlights the difficulty in classifying higher-rank dimension groups.

Abstract

The Borel complexity of the isomorphism problem for finite-rank unital simple dimension groups increases with rank. This implies that the isomorphism problems for the corresponding classes of Bratteli diagrams and LDA-groups also increase with rank.