THE VAN EST SPECTRAL SEQUENCE FOR HOPF ALGEBRAS

The van Est spectral sequence for Hopf algebras

Various aspects of the de Rham cohomology of Hopf algebras are discussed. In particular, it is shown that the de Rham cohomology of an algebra with the differentiable coaction of a cosemisimple Hopf algebra with trivial 0-th cohomology group, reduces to the de Rham cohomology of (co)invariant forms. Spectral sequences are discussed and the van Est spectral sequence for Hopf algebras is introduc...

Hopf Algebras up to Homotopy and the Bockstein Spectral Sequence

Anick proved that every q-mild Hopf algebra up to homotopy is isomorphic to the universal enveloping algebra of a chain Lie algebra. We provide a new proof, that involves extensive use of the Bockstein spectral sequence.

Spectral Sequences for the Classification of Extensions of Hopf Algebras

We construct spectral sequences which provide a way to compute the cohomology theory that classifies extensions of graded connected Hopf algebras over a commutative ring as described by William M. Singer. Specifically, for (A,B) an abelian matched pair of graded connected R-Hopf algebras, we construct a pair of spectral sequences relating H∗(B,A) to Ext∗,∗ B (R,Cotor ∗,∗ A (R,R)). To illustrate...

On the Coderivations of Some Hopf Algebras

Hopf algebras for ternary algebras and groups

We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters ...