Algebraic treatment of compactification on noncommutative tori

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.

8 pages, Latex, shortened version as accepted for publication in Physics Letters

References in corpus (1)

• Noncommutative Geometry and Matrix Theory: Compactification on Tori

Cited by in corpus (21)

• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Introduction to M(atrix) theory and noncommutative geometry
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Morita equivalence and duality
• Noncommutative Geometry from D0-branes in a Background B-field
• String Geometry and the Noncommutative Torus
• Dualities of the Matrix Model from T-Duality of the Type II String
• Gauge Bundles and Born-Infeld on the Noncommutative Torus
• Super Yang-Mills on the Noncomutative Torus
• Noncommutative String Theory, the R-Matrix, and Hopf Algebras
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• World Volume Noncommutativity versus Target Space Noncommutativity
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Derivatives and the Role of the Drinfel'd Twist in Noncommutative String Theory
• The Concept of a Noncommutative Riemann Surface
• Matrix Compactification On Orientifolds
• Orientifolds of Matrix theory and Noncommutative Geometry
• Noncommutative Geometry and Twisted Little-String Theories
• Projective Group Algebras
• Algebras, Derivations and Integrals
• Morita Equivalence and Interpolation of The Dirac-Born-infeld Theory on the Non-Commutative Torus