Abstract
We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.
Similar content being viewed by others
References
Beilinson, A. A., Bernstein, J. and Deligne, P.: Faisceaux Pervers, Astérisque 100, Soc. Math. France, 1982.
Bernstein, J. and Lunts, V.: Equivariant Sheaves and Functors, Lecture Notes in Math. 1578, Springer, Berlin, 1994.
Crane, L. and Frenkel, I. B.: Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35(10) (1994), 5136–5154.
Deligne, P.: Catégories tannakiennes, in The Grothendieck Festschrift, Vol. II, Progress inMath. 87, Birkhäuser, Boston, 1991, pp. 111–195.
Lusztig, G.: Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3(2) (1990), 447–498.
Lusztig, G.: Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4(2) (1991), 365–421.
Lusztig, G.: Introduction to Quantum Groups, Birkhäuser, Boston, 1993.
Lyubashenko, V. V.: Squared Hopf algebras, Mem. Amer. Math. Soc. 142(677) (1999), 184.
Majid, S.: Braided groups, J. Pure Appl. Algebra 86(2) (1993), 187–221.
Neuchl, M.: Representation theory of Hopf categories, Ph.D. Thesis. Available at: http://www.mathematik.uni-muenchen.de/~neuchl.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lyubashenko, V. The Triangulated Hopf Category n +SL(2). Applied Categorical Structures 10, 331–381 (2002). https://doi.org/10.1023/A:1016399419658
Issue Date:
DOI: https://doi.org/10.1023/A:1016399419658