20 Pages

Survey of Cross Product Bialgebras

WithYuri Bespalov, Bernhard Drabant

Recently a theoiy has been found providing a universal and (co-)modular co‐cyclic characterization of cross product bialgebras with cocycles and dual cocycles unifying all cross product bialgebra constructions known so far. The construction in particular covers all cross product bialgebras such as bi- or smash, doublecross and bicross product bialgebras as well as double biproduct and crossed product bialgebras with co-cycles Furthermore new types of cross product bialgebras are found within our constinction.