Kadjo, Gabriel
[UCL]
Vercruysse, Joost
[Université Libre de Bruxelles]
Gran, Marino
[UCL]
The purpose of this article is to prove that the category of cocommutative Hopf K-algebras, over a field K of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it contains a torsion theory whose torsion-free and torsion parts are given by the category of groups and by the category of Lie K-algebras, respectively.
- Andruskiewitsch, N., Devoto, J.: Extensions of Hopf algebras. Algebra i Analiz 7(1), 22–61 (1995)
- Barr Michael, Grillet Pierre A., van Osdol Donovan H., Exact Categories and Categories of Sheaves, ISBN:9783540056782, 10.1007/bfb0058579
- Borceux Francis, Bourn Dominique, Mal’cev, Protomodular, Homological and Semi-Abelian Categories, ISBN:9789048165513, 10.1007/978-1-4020-1962-3
- Borceux, F., Janelidze, G., Kelly, G.: Internal object actions. Comment. Math. Univ. Carol. 46(2), 235–255 (2005)
- Bourn Dominique, Normalization equivalence, kernel equivalence and affine categories, Lecture Notes in Mathematics (1991) ISBN:9783540547068 p.43-62, 10.1007/bfb0084212
- Bourn, D.: Normal functors and strong protomodularity. Theory and Applications of Categories 7(9), 205–218 (2000)
- Bourn Dominique, Gran Marino, Torsion theories in homological categories, 10.1016/j.jalgebra.2006.07.011
- Carboni A., Lambek J., Pedicchio M.C., Diagram chasing in Mal'cev categories, 10.1016/0022-4049(91)90022-t
- Cassidy C., Hébert M., Kelly G. M., Reflective subcategories, localizations and factorizationa systems, 10.1017/s1446788700023624
- Chirvăsitu Alexandru, On epimorphisms and monomorphisms of Hopf algebras, 10.1016/j.jalgebra.2009.12.025
- Dickson, S.: A torsion theory for abelian categories. Trans. Amer. Math. Soc. 86, 47–62 (1998)
- Duckerts Mathieu, Everaert Tomas, Gran Marino, A description of the fundamental group in terms of commutators and closure operators, 10.1016/j.jpaa.2012.02.022
- Everaert Tomas, Gran Marino, Protoadditive functors, derived torsion theories and homology, 10.1016/j.jpaa.2014.12.015
- Gran Marino, Rossi Valentina, Torsion theories and Galois coverings of topological groups, 10.1016/j.jpaa.2005.12.001
- Grunenfelder Luzius, Paré Robert, Families parametrized by coalgebras, 10.1016/0021-8693(87)90093-7
- Higgins P. J., Groups with Multiple Operators, 10.1112/plms/s3-6.3.366
- Janelidze George, Pure Galois theory in categories, 10.1016/0021-8693(90)90130-g
- Janelidze George, Márki László, Tholen Walter, Semi-abelian categories, 10.1016/s0022-4049(01)00103-7
- Milnor John W., Moore John C., On the Structure of Hopf Algebras, 10.2307/1970615
- Molnar Richard K, Semi-direct products of Hopf algebras, 10.1016/0021-8693(77)90208-3
- Nǎstǎsescu C., Torrecillas B., Torsion theories for coalgebras, 10.1016/0022-4049(94)00009-3
- Newman Kenneth, A correspondence between bi-ideals and sub-Hopf algebras in cocommutative Hopf algebras, 10.1016/0021-8693(75)90150-7
- Porst Hans-E., Limits and colimits of Hopf algebras, 10.1016/j.jalgebra.2010.10.014
- Shudo, T.: On strongly exact sequences of cocommutative hopf algebras. Hiroshima Mathematical Journal 18(1), 189–206 (1988)
- Street Ross, Quantum Groups : A Path to Current Algebra, ISBN:9780511618505, 10.1017/cbo9780511618505
- Sweedler, M.: Hopf algebras. Benjamin, New York (1969)
- Takeuchi Mitsuhiro, A correspondence between Hopf ideals and sub-Hopf algebras, 10.1007/bf01579722
- Vespa, C., Wambst, M.: On some properties of the category of cocommutative Hopf algebras. arXiv: 1502.04001
| Bibliographic reference |
Kadjo, Gabriel ; Vercruysse, Joost ; Gran, Marino. A torsion theory in the category of cocommutative Hopf algebras. In: Applied Categorical Structures, Vol. 24, p. 206-232 (2016) |
| Permanent URL |
http://hdl.handle.net/2078.1/158889 |
