# Ground states for generalized gauge actions on UHF algebras

## TL;DR

This paper characterizes ground and ceiling states for generalized gauge actions on UHF algebras, revealing their affine homeomorphism to unital AF algebra state spaces and exploring KMS-infinity states.

## Contribution

It provides a detailed description of ground and ceiling states for these actions, showing their affine homeomorphism to unital AF algebra state spaces and demonstrating the universality of this structure.

## Key findings

- Ground and ceiling states are affinely homeomorphic to unital AF algebra state spaces.
- Any pair of unital AF algebras can be realized as such states.
- Analysis of KMS-infinity states extends the understanding of equilibrium states.

## Abstract

We describe the structure of ground states and ceiling states for generalized gauge actions on an UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addtion, we study the KMS-infinity states.