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Inhomogeneous Yang-Mills Algebras

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Abstract

We determine all inhomogeneous Yang–Mills algebras and super Yang–Mills algebras which are Koszul. Following a recent proposal, a non-homogeneous algebra is said to be Koszul if the homogeneous part is Koszul and if the PBW property holds. In this letter, the homogeneous parts are the Yang–Mills algebra and the super Yang–Mills algebra.

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References

  1. Berger R. (2001). Koszulity for nonquadratic algebras. J. Algebra 239:705–734

    Article  MATH  MathSciNet  Google Scholar 

  2. Berger R., Dubois-Violette M., Wambst M. (2003). Homogeneous algebras. J. Algebra 261:172–185

    Article  MATH  MathSciNet  Google Scholar 

  3. Berger, R., Ginzburg, V.: Higher symplectic reflection algebras and non-homogeneous N-Koszul property. J. Algebra (in press) math.RA/0506093

  4. Berger, R., Marconnet, N.: Koszul and Gorenstein properties for homogeneous algebras. Alg. Rep. Theory (in press) math.QA/0310070

  5. Braverman A., Gaitsgory D. (1996). Poincaré–Birkhoff–Witt theorem for quadratic algebras of Koszul type. J. Algebra 181:315–328

    Article  MATH  MathSciNet  Google Scholar 

  6. Connes A., Dubois-Violette M. (2002). Yang–Mills algebra. Lett. Math. Phys. 61:149–158

    Article  MATH  MathSciNet  Google Scholar 

  7. Connes, A., Dubois-Violette, M.: Yang–Mills and some related algebras. Rigorous Quantum Field Theory. (2004) math-ph/0411062

  8. Dubois-Violette M. (2005). Graded algebras and multilinear forms. C.R. Acad. Sci. Paris, Ser. I 341:719–724

    MATH  MathSciNet  Google Scholar 

  9. Etingof P., Ginzburg V. (2002). Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-chandra homomorphism. Invent. Math. 147:243–348

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Floystad G., Vatne, J.E.: PBW-deformations of N-Koszul algebras. J. Algebra (in press) math.RA/0505570

  11. Goodearl K.R. (1979). Von Neumann regular rings. Pitman, London

    MATH  Google Scholar 

  12. Polishchuk, A., Positselski, L.: Quadratic algebras. AMS University Lectures Series American Mathematics Society, (2005)

  13. Weibel C.A. (1994). An introduction to homological algebra. Cambridge University Press, Cambridge

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculté des Sciences et Techniques, LaMUSE, 23 rue P. Michelon, F-42023, Saint-Etienne Cedex 2, France

    Roland Berger

  2. Laboratoire de Physique Théorique, UMR 8627, Université Paris XI, Bâtiment 210, F-91 405, Orsay Cedex, France

    Michel Dubois-Violette

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  1. Roland Berger
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  2. Michel Dubois-Violette
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Correspondence to Michel Dubois-Violette.

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Berger, R., Dubois-Violette, M. Inhomogeneous Yang-Mills Algebras. Lett Math Phys 76, 65–75 (2006). https://doi.org/10.1007/s11005-006-0075-5

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  • DOI: https://doi.org/10.1007/s11005-006-0075-5

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