Spectral Sequences for the Classification of Extensions of Hopf Algebras

Abstract

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 connectedR-Hopf algebras, we construct a pair of spectral sequences relatingH*(B,A) to Ext*,*B(R,Cotor*,*A(R,R)). To illustrate these spectral sequences, we examine the special case ofBa monogenic graded connected Hopf algebra and also analyze an extension of Hopf algebras given by James P. Lin.