Note on bi-exactness for creation operators on Fock spaces

TL;DR

This paper introduces a new concept of bi-exactness for creation operators on various Fock spaces, generalizing previous work and providing new examples and proofs related to solid actions and free wreath product groups.

Contribution

It generalizes bi-exactness to full, symmetric, and anti-symmetric Fock spaces, expanding the understanding of solid actions and their applications.

Findings

New examples of solid actions identified

Provided new proofs for existing solid actions

Studied free wreath product groups in this context

Abstract

In this note, we introduce and study a notion of bi-exactness for creation operators acting on full, symmetric and anti-symmetric Fock spaces. This is a generalization of our previous work, in which we studied the case of anti-symmetric Fock spaces. As a result, we obtain new examples of solid actions as well as new proofs for some known solid actions. We also study free wreath product groups in the same context.