Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 6 (1999), No. 1, Page 181-215
We present a construction of non-trivial self-dual Hopf algebras over a field $\k$ obtained by a double extension process. The construction is not symmetric: it involves a 2-cocycle which, under a certain coboundary condition, disappears in the dual structure. We present several explicit examples in low dimensions; we recover families of examples introduced by S. Gelaki and R. Williams.