On an invariant-theoretic description of the lambda algebra (Q817051)

Let \(p\) be an odd prime, \(\mathbb{F}_p\) the field of \(p\) elements and \(E_n\) an elementary abelian \(p\)-group of rank \(n\). The Borel subgroup \(B_n\) of the general linear group \(\text{Gl}_n(\mathbb{F}_p)\) acts on the localization, \(S^{-1}H^*(BE_n; \mathbb{F}_p)\), of \(H^*(BE_n;\mathbb{F}_p)\), with respect to the multiplicatively closed subset \(S\) generated by elements of degree 2 of \(H^*(BE_n;\mathbb{F}_p)\). Let \(\Delta_n=(S^{-1} H^*(BE_n;\mathbb{F}_p))^{B_n}\), \(\Delta=\bigoplus_{n\geq 0}\Delta_n\) where \(\Delta_0=\mathbb{F}_p\). The author constructs a differential graded algebra, as a subalgebra of a quotient of \(\Delta\), which is isomorphic to the mod \(p\) Lambda algebra. This generalizes a work of L. A. Lomonaco for the case \(p=2\).