The near-Hopf ring structure on the integral cohomology of 1-connected Lie groups

TL;DR

This paper explores the near-Hopf ring structure of the integral cohomology of 1-connected exceptional Lie groups, building on previous work that described their cohomology rings and algebraic structures over finite fields.

Contribution

It introduces the near-Hopf ring structure on the integral cohomology of these Lie groups, extending prior descriptions of their cohomology rings and algebraic structures.

Findings

Explicit description of the near-Hopf ring structure on H*(G)

Extension of previous cohomology ring results to near-Hopf ring context

Enhanced understanding of algebraic structures in Lie group cohomology

Abstract

Let G be an exceptional Lie group with a maximal torus T. Based on Schubert calculus on the flag manifold G/T we have described the integral cohomology ring H*(G) by explicitely constructed generators in [DZ2], and determined the structure of H*(G;F_{p}) as a Hopf algebra over the Steenrod algebra in[DZ3]. In this sequel to [DZ2], [DZ3] we obtain the near--Hopf ring structure on H*(G).