Algebraic treatment of compactification on noncommutative tori

TL;DR

This paper investigates the conditions for compactifying M theory on noncommutative tori using algebraic methods, providing explicit solutions within the algebra of projective representations.

Contribution

It introduces an algebraic framework for analyzing M theory compactification on noncommutative tori and explicitly constructs solutions using projective representation algebras.

Findings

Explicit solutions for compactification conditions

Algebraic characterization of noncommutative tori

Application of projective representation algebra

Abstract

In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori. The main tool used for this analysis is the algebra A(Z^D) of the projective representations of the abelian group Z^D. We exhibit the explicit solutions in the space of the multiplication algebra of A(Z^D), that is the algebra generated by right and left multiplications.