Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well-known results from group theory. The uniqueness of a Krull-Schmidt-Remak type decomposition is proved for semisimple completely reducible Hopf algebras.
@article{bwmeta1.element.doi-10_2478_s11533-011-0042-y,
author = {Sebastian Burciu},
title = {On complements and the factorization problem of Hopf algebras},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {905-914},
zbl = {1263.16031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0042-y}
}
Sebastian Burciu. On complements and the factorization problem of Hopf algebras. Open Mathematics, Tome 9 (2011) pp. 905-914. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0042-y/
[1] Agore A.L., Crossed product of Hopf algebras (in preparation) | Zbl 06198152
[2] Burciu S., Coset decomposition for semisimple Hopf algebras, Comm. Algebra, 2009, 37(10), 3573–3585 http://dx.doi.org/10.1080/00927870902828496 | Zbl 1193.16025
[3] Burciu S., Normal Hopf subalgebras of semisimple Hopf algebras, Proc. Amer. Mat. Soc., 2009, 137(12), 3969–3979 http://dx.doi.org/10.1090/S0002-9939-09-09965-1 | Zbl 1191.16031
[4] Kassel C., Quantum Groups, Grad. Texts in Math., 155, Springer, New York, 1995
[5] Majid S., Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, 1995 http://dx.doi.org/10.1017/CBO9780511613104 | Zbl 0857.17009
[6] Masuoka A., Coideal subalgebras in finite Hopf algebras, J. Algebra, 1994, 163(3), 819–831 http://dx.doi.org/10.1006/jabr.1994.1047 | Zbl 0809.16045
[7] Montgomery S., Hopf Algebras and their Actions on Rings, CBMS Regional Conf. Ser. in Math., 82, American Mathematical Society, Providence, 1993
[8] Natale S., On semisimple Hopf algebras of low dimension, AMA Algebra Montp. Announc., 2003, #6 | Zbl 1060.16040
[9] Robinson D.J.S., A Course in the Theory of Groups, Grad. Texts in Math., 80, Springer, New York-Berlin, 1982 | Zbl 0483.20001