Heisenberg modules over real multiplication noncommutative tori and related algebraic structures

TL;DR

This paper reviews the role of Heisenberg groups in defining algebraic structures on noncommutative two-tori with real multiplication, highlighting their mathematical significance.

Contribution

It provides a comprehensive review of how Heisenberg groups contribute to the algebraic framework of noncommutative tori with real multiplication.

Findings

Heisenberg groups are central to the algebraic structures of noncommutative tori.

Real multiplication influences the structure of noncommutative two-tori.

The paper clarifies the connection between algebraic structures and noncommutative geometry.

Abstract

We review some aspects of the theory of noncommutative two-tori with real multiplication focusing on the role played by Heisenberg groups in the definition of algebraic structures associated to these noncommutative spaces.