On Hopf algebras of dimension $p^3$

Details On Hopf algebras of dimension $p^3$ On Hopf algebras of dimension $p^3$

2004-01-19

arxiv.org/abs/math/0401232v2

Tsukuba J. Math. 29 (2005), no. 1, 259--284

Mathematics

Quantum Algebra

27 pages, minor changes. Accepted for publication in the Tsukuba Journal of Mathematics

Scientific paper

We discuss some general results on finite-dimensional Hopf algebras over an algebraically closed field k of characteristic zero and then apply them to Hopf algebras H of dimension p^{3} over k. There are 10 cases according to the group-like elements of H and H^{*}. We show that in 8 of the 10 cases, it is possible to determine the structure of the Hopf algebra. We give also a partial classification of the quasitriangular Hopf algebras of dimension p^{3} over k, after studying extensions of a group algebra of order p by a Taft algebra of dimension p^{2}. In particular, we prove that every ribbon Hopf algebra of dimension p^{3} over k is either a group algebra or a Frobenius-Lusztig kernel. Finally, using some previous results on bounds for the dimension of the first term H_{1} in the coradical filtration of H, we give the complete classification of the quasitriangular Hopf algebras of dimension 27.

Affiliated with

Also associated with

No associations

Rating

On Hopf algebras of dimension $p^3$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Hopf algebras of dimension $p^3$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Hopf algebras of dimension $p^3$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-569963