Counting arguments for Hopf algebras of low dimension

SONIA LUJAN NATALE; ANDRUSKIEWITSCH

TSUKUBA JOURNAL OF MATHEMATICS

Tsukuba University

Lugar: Tsukuba; Año: 2000 vol. 25 p. 187 - 201

0387-4982

We give the classification of Hopf algebras H over an algebraically closed field of characteristic zero of certain dimensions. If dim H is 15 or 35, H is the group algebra of a cyclic group. If dim H is 21, then H is semisimple and is isomorphic to a group algebra or its dual. If dim H is 25 or 49, then either H is semisimple and a group algebra, or it is pointed and a Taft algebra. The proofs use some results of Nichols on coradical filtrations. An Appendix classifies pointed H of dimension pq^2, p, q distinct primes, and shows that a semisimple H of dimension 45 is a group algebra.