A construction of the universal classes for algebraic groups with the twisting spectral sequence

TL;DR

This paper introduces a new proof for the existence of universal classes in algebraic groups by applying ideas from strict polynomial bifunctors and the twisting spectral sequence.

Contribution

It provides a novel proof of universal classes construction using the framework of strict polynomial bifunctors and the twisting spectral sequence.

Findings

New proof of universal classes existence

Application of strict polynomial bifunctors

Utilization of the twisting spectral sequence

Abstract

In this article, we apply some ideas developped by M. Cha{\l}upnik to the framework of strict polynomial bifunctors. This allows us to get a new proof of the existence of the `universal classes' originally constructed by the author.