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Cross Product Bialgebras Part II

2001; Elsevier BV; Volume: 240; Issue: 2 Linguagem: Inglês

10.1006/jabr.2000.8631

1090-266X

Yuri Bespalov, Bernhard Drabant,

Homotopy and Cohomology in Algebraic Topology

This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent (co-)modular (co-)cyclic formulation. All known examples as for instance bi- or smash, doublecross and bicross product bialgebras as well as double biproduct bialgebras and bicrossed or cocycle bicross product bialgebras are now united within a single theory. Furthermore our construction yields various novel types of cross product bialgebras.