Some examples of non-semisimple and non-pointed Hopf algebras of dimension 16
by
Corina Calinescu
Institute of Mathematics of the Romanian Academy

Recently there has been a renewed interest in the classification problem of Hopf algebras of a given dimension over an algebraically closed field of characteristic zero. The pointed Hopf algebras of dimension 16 were classified by S. Caenepeel, S. Dascalescu and S. Raianu and the semisimple Hopf algebras of the same dimension by E. Kashina.
We present some examples of Hopf algebras of dimension 16 which are neither pointed nor semisimple and whose coradical is the non-trivial semisimple Hopf algebra of dimension 8. These are obtained using the principle of lifting of quantum linear spaces proposed by N. Andruskiewitsch and H.J. Schneider. We remark that we can get the above mentioned examples by the Ore extensions construction described by M. Beattie, S. Dascalescu and L. Grunenfelder.

Date received: August 7, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafe-57.