On complements and the factorization problem of Hopf algebras

Sebastian Burciu

Open Mathematics (2011)

  • Volume: 9, Issue: 4, page 905-914
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Sebastian Burciu. "On complements and the factorization problem of Hopf algebras." Open Mathematics 9.4 (2011): 905-914. <http://eudml.org/doc/269303>.

@article{SebastianBurciu2011,
abstract = {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.},
author = {Sebastian Burciu},
journal = {Open Mathematics},
keywords = {Normal Hopf subalgebras; Semi-direct product; Internal tensor product; normal Hopf subalgebras; semi-direct products; internal tensor products; semisimple Hopf algebras; Krull-Schmidt-Remak type decompositions; completely reducible Hopf algebras; normal factorizations},
language = {eng},
number = {4},
pages = {905-914},
title = {On complements and the factorization problem of Hopf algebras},
url = {http://eudml.org/doc/269303},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Sebastian Burciu
TI - On complements and the factorization problem of Hopf algebras
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 905
EP - 914
AB - 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.
LA - eng
KW - Normal Hopf subalgebras; Semi-direct product; Internal tensor product; normal Hopf subalgebras; semi-direct products; internal tensor products; semisimple Hopf algebras; Krull-Schmidt-Remak type decompositions; completely reducible Hopf algebras; normal factorizations
UR - http://eudml.org/doc/269303
ER -

References

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  1. [1] Agore A.L., Crossed product of Hopf algebras (in preparation) Zbl06198152
  2. [2] Burciu S., Coset decomposition for semisimple Hopf algebras, Comm. Algebra, 2009, 37(10), 3573–3585 http://dx.doi.org/10.1080/00927870902828496 Zbl1193.16025
  3. [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 Zbl1191.16031
  4. [4] Kassel C., Quantum Groups, Grad. Texts in Math., 155, Springer, New York, 1995 
  5. [5] Majid S., Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, 1995 http://dx.doi.org/10.1017/CBO9780511613104 Zbl0857.17009
  6. [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 Zbl0809.16045
  7. [7] Montgomery S., Hopf Algebras and their Actions on Rings, CBMS Regional Conf. Ser. in Math., 82, American Mathematical Society, Providence, 1993 
  8. [8] Natale S., On semisimple Hopf algebras of low dimension, AMA Algebra Montp. Announc., 2003, #6 Zbl1060.16040
  9. [9] Robinson D.J.S., A Course in the Theory of Groups, Grad. Texts in Math., 80, Springer, New York-Berlin, 1982 Zbl0483.20001

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