The cohomology of S(n,k) relavent to Morava stablizer algebra

TL;DR

This paper introduces a new filtration on the Hopf algebra S(n,k), leading to a spectral sequence that facilitates the computation of its cohomology in specific cases relevant to Morava stabilizer algebra.

Contribution

It redefines an increasing filtration on S(n,k) and applies a spectral sequence to compute its cohomology for particular parameters and primes.

Findings

Computed $H^{*,*}S(n,n)$ at prime 2

Computed $H^{*,*}S(3,2)$ at prime 3

Computed $H^{*,*}S(4,2)$ at prime p≥5

Abstract

In this paper we redefine an increasing filtration on the the Hopf algebra S(n,k), From which we get a spectral sequence called May spectral sequence. As an application we computed $H^{*,*}S(n,n)$ at prime 2, $H^{*,*}S(3,2)$ at prime 3 and $H^{*,*}S(4,2)$ at prime $p\geqslant 5$