# A concise review on pseudo-bosons, pseudo-fermions and their relatives

## TL;DR

This paper reviews the recent developments in pseudo-bosons and pseudo-fermions, including their definitions, properties, and finite-dimensional extensions, with detailed examples.

## Contribution

It provides a concise overview of the foundational concepts and recent advances in pseudo-bosons and pseudo-fermions, highlighting finite-dimensional extensions and examples.

## Key findings

- Summary of basic definitions and facts for pseudo-bosons and pseudo-fermions
- Introduction of finite-dimensional biorthogonal basis extensions
- Detailed examples illustrating theoretical concepts

## Abstract

We review some basic definitions and few facts recently established for $\D$-pseudo bosons and for pseudo-fermions. We also discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space. Some examples are described in details.