Cohomology of finite-dimensional connected cocommutative Hopf algebras
Let \(A\) be a finite-dimensional cocommutative graded connected Hopf algebra. The May spectral sequence is obtained by filtering the bar construction for \(A\) by the filtration induced by filtering \(A\) by powers of its augmentation ideal. The authors give a sufficient condition for the existence of some finite \(r\) such that \(E_ r = E_ \infty\). As a corollary they show that the May spectral sequence stops at a finite state for the subalgebras of the Steenrod algebra \(A(n)\) for \(p = 2\) and \(P(n)\) for \(p > 2\). They also consider the Ivanovskij spectral sequence obtained by filtering the cobar construction on \(A\) by copowers of the unit co-ideal. They show that this spectral sequence stops at \(E_ r\) for some finite \(r\).
finite-dimensional cocommutative graded connected Hopf algebra
scientific article; zbMATH DE number 612141
scientific article