Advertisement

A Note on the Categorification of Lie Algebras

  • Isar Goyvaerts
  • Joost Vercruysse
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 36)

Abstract

In this short note we study Lie algebras in the framework of symmetric monoidal categories. After a brief review of the existing work in this field and a presentation of earlier studied and new examples, we examine which functors preserve the structure of a Lie algebra.

Keywords

Hopf Algebra Monoidal Category Symmetric Monoidal Category Braided Monoidal Category Baxter Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bathurin, Y., Fischman, D., Montgomery, S.: On the generalized Lie structure of associative algebras. Israel J. Math. 96, 27–48 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Caenepeel, S., Goyvaerts, I.: Monoidal Hom-Hopf algebras. Comm. Algebra 39, 2216–2240 (2011)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Fischman, D., Montgomery, S.: A Schur double centralizer theorem for cotriangular Hopf algebras and generalized Lie algebras. J. Algebra 168, 594–614 (1994)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Goyvaerts, I., Vercruysse, J.: On the duality of generalized Lie and Hopf algebras, in preparationGoogle Scholar
  5. 5.
    Hartwig, J., Larsson, D., Silvestrov, S.: Deformations of Lie algebras using σ-derivations. J. Algebra 295, 314–361 (2006)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Janssen, K., Vercruysse, J.: Multiplier bi- and Hopf algebras. J. Algebra Appl. 9, 275–303 (2010)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Majid, S.: Quantum and braided-Lie algebras. J. Geom. Phys. 13, 307–356 (1994)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Michaelis, W.: Lie Coalgebras. Adv. Math. 38, 1–54 (1980)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Pareigis, B.: On Lie algebras in the category of Yetter-Drinfeld modules. Appl. Categorical Struct. 6, 151–175 (1998)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Takeuchi, M.: Survey of braided Hopf algebras. Contemp. Math. 267, 301–323 (2000)CrossRefGoogle Scholar
  11. 11.
    Van Daele, A.: Multiplier Hopf algebras. Trans. Am. Math. Soc. 342(2), 917–932 (1994)MATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselBelgium
  2. 2.Département de MathématiquesUniversité Libre de BruxellesBruxellesBelgium

Personalised recommendations