Local versus global subtleties of projective representations

TL;DR

This paper reviews the nuanced differences between local and global properties of projective representations, emphasizing the role of algebraic topology in their analysis and providing rigorous theorems to clarify these subtleties.

Contribution

It offers a rigorous analysis contrasting local and global aspects of projective representations and demonstrates the application of algebraic topology tools in their characterization.

Findings

Clarifies the interplay between local and global properties of projective representations

Provides necessary theorems for understanding projective representations

Demonstrates algebraic topology tools in representation analysis

Abstract

In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main necessary theorems. We discuss the implementation of useful algebraic topology tools to characterize representations.