Geometrical and Algebraic Structures in Quantum Hall Systems

TL;DR

This paper reviews the mathematical frameworks that describe the geometrical and algebraic structures underlying quantum Hall systems, focusing on their role in quantization of Hall conductivity.

Contribution

It provides a comprehensive overview of the geometrical and algebraic structures influencing quantum Hall effects, including finite size and boundary condition considerations.

Findings

Analysis of geometrical structures in Hall systems

Discussion of algebraic structures controlling quantization

Insights into finite size and boundary effects

Abstract

We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic structures controlling possibly the integral or fractional quantization of the Hall conductivity are discussed.