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The Quantum Group of a Preregular Multilinear Form

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We describe the universal quantum group preserving a preregular multilinear form, by means of an explicit finite presentation of the corresponding Hopf algebra.

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References

  1. Banica T., Vergnioux R.: Fusion rules for quantum reflection groups. J. Noncommut. Geom. 3, 327–359 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Belitskii G., Sergeichuk V.: Congruence of multilinear forms. Linear Algebra Appl. 418, 751–762 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bichon J.: Cosovereign Hopf algebras. J. Pure Appl. Algebra 157(2-3), 121–133 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bichon J.: The representation category of the quantum group of a non-degenerate bilinear form. Commun. Algebra 31(10), 4831–4851 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bichon J.: Free wreath product by the quantum permutation group. Algebra Represent. Theory 7, 343–362 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chervov A., Falqui G., Rubtsov V.: Algebraic properties of Manin matrices. I. Adv. Appl. Math. 43(3), 239–315 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Connes A., Moscovici H.: Hopf algebras, cyclic cohomology and the transverse index theorem. Commun. Math. Phys. 198, 199–246 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Connes A., Moscovici H.: Cyclic cohomology and Hopf algebras. Lett. Math. Phys. 48, 97–108 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Connes A., Moscovici H.: Cyclic cohomology and Hopf algebra symmetry. Lett. Math. Phys. 53, 1–28 (2000)

    Article  MathSciNet  Google Scholar 

  10. Crainic M.: cohomology of Hopf algebras. J. Pure Appl. Algebra 166, 29–66 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Dubois-Violette M.: Multilinear forms and graded algebras. J. Algebra 317, 198–225 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dubois-Violette, M.: Noncommutative coordinate algebras. In: Blanchard, E. (ed.) Quanta of Maths, dédié à à A. Connes. In: Clay Mathematics Proceedings, pp. 171–199. Clay Mathematics Institute (2010)

  14. Dubois-Violette M., Launer G.: The quantum group of a non-degenerate bilinear form. Phys. Lett. B 245(2), 175–177 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. Manin Yu.I.: Quantum groups and noncommutative geometry Université de Montréal. Centre de Recherches Mathématiques, Montréal (1988)

    Google Scholar 

  16. Riehm, C.: The equivalence of bilinear forms. J. Algebra 31, 45–66 (1974)

    Google Scholar 

  17. Rosso M.: Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non-commutatif. Duke Math. J. 61, 11–40 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  18. Woronowicz S.L.: Compact matrix pseudogroups. Commun. Math. Phys. 111, 613–665 (1987)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. Woronowicz S.L.: Tannaka–Krein duality for compact matrix pseudogroups. Twisted SU(N) groups. Invent. Math. 93, 35–76 (1988)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Correspondence to Michel Dubois-Violette.

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Bichon, J., Dubois-Violette, M. The Quantum Group of a Preregular Multilinear Form. Lett Math Phys 103, 455–468 (2013). https://doi.org/10.1007/s11005-012-0603-4

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  • DOI: https://doi.org/10.1007/s11005-012-0603-4

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