An A∞-structure on the Cohomology Ring of the Symmetric Group Sp with Coefficients in 𝔽p

Let p be a prime. Let 𝔽pSp be the group algebra of the symmetric group over the finite field with p elements 𝔽p. Let 𝔽p be the trivial 𝔽pSp-module. We choose a projective resolution PRes𝔽p of the module 𝔽p and equip the Yoneda algebra Ext𝔽pSp∗(𝔽p,𝔽p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Ext}^{\ast }_{\mathbb{F}_{p} S_{p}}\left( \mathbb{F}_{p}, \mathbb{F}_{p}\right)$\end{document} with an A∞-structure such that Ext𝔽pSp∗(𝔽p,𝔽p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Ext}^{\ast }_{\mathbb{F}_{p} S_{p}}\left( \mathbb{F}_{p}, \mathbb{F}_{p}\right)$\end{document} becomes a minimal model in the sense of Kadeishvili of the dg-algebra Hom𝔽pSp∗(PRes𝔽p,PRes𝔽p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Hom}^{\ast }_{\mathbb{F}_{p} S_{p}}\left(PRes \mathbb{F}_{p}, PRes \mathbb{F}_{p}\right)$\end{document}.