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Noncommutative Physics on Lie Algebras, (ℤ2)n Lattices and Clifford Algebras

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Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type cocycle twist, such as the noncommutative torus, θ-spaces and Clifford algebras. The latter are noncommutative deformations of the finite lattice (ℤ2)n and we compute their noncommutative de Rham cohomology and moduli of solutions of Maxwell’s equations. We exactly quantize noncommutative U(1)-Yang-Mills theory on ℤ2 × ℤ2 in a path integral approach.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, London, El 4NS, UK

    Shahn Majid

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  1. Shahn Majid
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Majid, S. (2004). Noncommutative Physics on Lie Algebras, (ℤ2)n Lattices and Clifford Algebras. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_31

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_31

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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