Algebraic treatment of compactification on noncommutative tori

1998/01/31 by R. Casalbuoni · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Algebra over a field #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Compactification (mathematics) #Mathematical analysis #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Pure mathematics #hep-th

paper · pdf · doi:10.1016/s0370-2693(98)00542-5

published as Phys.Lett. B431 (1998) 69-72 · 8 pages, Latex, shortened version as accepted for publication in Physics Letters

arxiv created 1998/04/27 · openalex publication_date 1998/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• String theory dynamics in various dimensions
• Dirichlet Branes and Ramond-Ramond Charges
• Mtheory as a matrix model: A conjecture
• D-brane field theory on compact spaces
• Noncommutative geometry and Matrix theory

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