Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T09:46:13.597Z Has data issue: false hasContentIssue false

STRUCTURE OF CORADICAL FILTRATION AND ITS APPLICATION TO HOPF ALGEBRAS OF DIMENSION pq

Published online by Cambridge University Press:  01 May 2008

DAIJIRO FUKUDA*
Affiliation:
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper contributes to the classification problem of pq dimensional Hopf algebras H over an algebraically closed field k of characteristic 0, where p, q are odd primes. It is shown that such Hopf algebras H are semisimple for the pairs of odd primes (p, q)=(3,11),(3,13),(3,19),(5,17),(5,19),(5,23),(5,29),(7,17),(7,19),(7,23),(7,29),(11,29),(13,29).

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Andruskiewitsch, N. and Natale, S.Counting arguments for Hopf algebras of low dimension, Tsukuba J. Math. 25 (2001), No. 1, 187201.CrossRefGoogle Scholar
2.Beattie, M. and Dăscălescu, S., Hopf algebras of dimension 14, J. London Math. Soc. (2) 69 (2004), No. 1, 6578.CrossRefGoogle Scholar
3.Dăscălescu, S., Năstăsescu, C. and Raianu, Ş., Hopf algebras: an introduction, Monographs in Pure and Applied Math. 235 (Marcel Dekker, 2000).Google Scholar
4.Etingof, P. and Gelaki, S.Semisimple Hopf algebras of dimension pq are trivial, J. Algebra 210 (1998), No. 2, 664669.CrossRefGoogle Scholar
5.Etingof, P. and Gelaki, S.On Hopf algebras of dimension pq, J. Algebra 277 (2004), No. 2, 668674.CrossRefGoogle Scholar
6.Montgomery, S., Hopf algebras and their actions on rings, CBMS, Vol. 82 (AMS, 1993).CrossRefGoogle Scholar
7.Ng, S.-H., Non-semisimple Hopf algebras of dimension p2, J. Algebra 255 (2002), No. 1, 182197.CrossRefGoogle Scholar
8.Ng, S.-H., Hopf algebras of dimension pq, J. Algebra 276 (2004), No. 1, 399406.CrossRefGoogle Scholar
9.Ng, S.-H., Hopf algebras of dimension 2p, Proc. Amer. Math. Soc. 133 (2005), 22372242.CrossRefGoogle Scholar
10.Ştefan, D., Hopf subalgebras of pointed Hopf algebras and applications, Proc. Amer. Math. Soc. 125 (1997), No. 11, 31913193.CrossRefGoogle Scholar