On complements and the factorization problem of Hopf algebras

• Autorzy: Sebastian Burciu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Normal Hopf subalgebras; Semi-direct product; Internal tensor product

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 905-914

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Sebastian Burciu

Bibliografia

• [1] Agore A.L., Crossed product of Hopf algebras (in preparation)
• [2] Burciu S., Coset decomposition for semisimple Hopf algebras, Comm. Algebra, 2009, 37(10), 3573–3585 http://dx.doi.org/10.1080/00927870902828496
• [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
• [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
• [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
• [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
• [9] Robinson D.J.S., A Course in the Theory of Groups, Grad. Texts in Math., 80, Springer, New York-Berlin, 1982

Identyfikatory

DOI

10.2478/s11533-011-0042-y