1993/07/22 by J. Madore, J. MADORE, J. Mourad +1 · 20 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic and Geometric Analysis #Commutative property #Extension (predicate logic) #Manifold (fluid mechanics) #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum differential calculus #Tensor product #gr-qc
paper · pdf · doi:10.1142/s0218271894000332
published in International Journal of Modern Physics D 03(01), 221-224 (World Scientific) · 4 pages. Talk delivered at the 'journées Relativistes 93'
arxiv created 1993/07/22 · openalex publication_date 1994/03/01 · arxiv updated 2011/04/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of n×n complex matrices. Noncommutative geometry is used to formulate an extension of the Einstein-Hilbert action. The result is shown to be equivalent to the usual Kaluza-Klein theory with the manifold SU n as an internal space, in a truncated approximation.