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Modules and Comodules pp 47–64Cite as

On Nichols Algebras with Generic Braiding

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Part of the book series: Trends in Mathematics ((TM))

Abstract

We extend the main result of [AS3] to braided vector spaces of generic diagonal type using results of Heckenberger.

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References

  1. N. Andruskiewitsch and H.-J. Schneider, Finite quantum groups and Cartan matrices. Adv. Math 54, 1–45 (2000).

    Article  MathSciNet  Google Scholar 

  2. N. Andruskiewitsch and H.-J. Schneider, Pointed Hopf Algebras, in “New directions in Hopf algebras”, 1–68, Math. Sci. Res. Inst. Publ. 43, Cambridge Univ. Press, Cambridge, 2002.

    Google Scholar 

  3. N. Andruskiewitsch and H.-J. Schneider, A characterization of quantum groups. J. Reine Angew. Math. 577, 81–104 (2004).

    MathSciNet  MATH  Google Scholar 

  4. I. Angiono, Álgebras de Nichols sobre grupos abelianos, Tesis de licenciatura, Univ. Nac. de La Plata (2007). Available at http://www.mate.uncor.edu/angiono.

    Google Scholar 

  5. N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris, 1968.

    MATH  Google Scholar 

  6. M. Hall, A basis for free Lie rings and higher commutators in free groups, Proc. Am. Math. Soc., 1, 575–581 (1950).

    Article  MATH  Google Scholar 

  7. I. Heckenberger, The Weyl groupoid of a Nichols algebra of diagonal type, Inventiones Math. 164, 175–188 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  8. I. Heckenberger, Weyl equivalence for rank 2 Nichols algebras of diagonal type, Ann. Univ. Ferrara — Sez. VII — Sc. Mat., vol. LI, pp. 281–289 (2005).

    MathSciNet  Google Scholar 

  9. I. Heckenberger, Rank 2 Nichols algebras with finite arithmetic root system. Algebr. Represent. Theory, to appear.

    Google Scholar 

  10. V. Kharchenko, A quantum analog of the Poincaré-Birkhoff-Witt theorem, Algebra and Logic, 38, (1999), 259–276.

    Article  MathSciNet  Google Scholar 

  11. V. Kac, Infinite-dimensional Lie algebras, 3rd Edition, Cambridge University Press, Cambridge, 1990.

    MATH  Google Scholar 

  12. M. Rosso, Quantum groups and quantum shuffles, Invent. Math. 133 (1998), 399–416.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Rosso, Lyndon words and Universal R-matrices, talk at MSRI, October 26, 1999, available at http://www.msri.org; Lyndon basis and the multiplicative formula for R-matrices, preprint (2003).

  14. V. Serganova, On generalizations of root systems, Commun. Algebra 24 (1996), 4281–4299.

    Article  MathSciNet  MATH  Google Scholar 

  15. A.I. Shirshov, On free Lie rings, Mat. Sb., 45(87), No. 2, 113–122 (1958).

    MathSciNet  Google Scholar 

  16. S. Ufer, PBW bases for a class of braided Hopf algebras, J. Alg. 280 (2004) 84–119.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Facultad of Matemática, Astronomía y Física, Universidad Nacional of Córdoba CIEM — CONICET, (5000) Ciudad Universitaria, Córdoba, Argentina

    Nicolás Andruskiewitsch & Iván Ezequiel Angiono

Authors
  1. Nicolás Andruskiewitsch
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  2. Iván Ezequiel Angiono
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK

    Tomasz Brzeziński

  2. Departamento de Alxebra, Universidade de Santiago, 15782, Santiago de Compostela, Spain

    José Luis Gómez Pardo

  3. Instituto de Matemática e Estatística da, Universidade de São Paulo (IME-USP), Rua do Matão, 1010 Cidade Universitária, CEP 05508-090, São Paulo - SP, Brasil

    Ivan Shestakov

  4. Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland,UK

    Patrick F. Smith

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Andruskiewitsch, N., Angiono, I.E. (2008). On Nichols Algebras with Generic Braiding. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_3

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