9 research outputs found
The Classification of All Crossed Products
Using the computational approach introduced in [Agore A.L., Bontea C.G.,
Militaru G., J. Algebra Appl. 12 (2013), 1250227, 24 pages, arXiv:1207.0411] we
classify all coalgebra split extensions of by , where is
the cyclic group of order and is Sweedler's -dimensional Hopf
algebra. Equivalently, we classify all crossed products of Hopf algebras by explicitly computing two classifying objects: the cohomological
'group' and
the set of types of isomorphisms of all crossed products .
More precisely, all crossed products are described by
generators and relations and classified: they are -dimensional quantum
groups , parameterized by the set of all pairs consisting of an arbitrary unitary map and an -th root
of . As an application, the group of Hopf algebra
automorphisms of is explicitly described
Crossed Product of Cyclic Groups
All crossed products of two cyclic groups are explicitly described using
generators and relations. A necessary and sufficient condition for an extension
of a group by a group to be a cyclic group is given.Comment: To appear in Czechoslovak Mathematical Journa