Algebras and Representation Theory

, Volume 17, Issue 5, pp 1553–1585 | Cite as

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

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Abstract

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 \(\mathrm{Ext}^{\ast }_{\mathbb{F}_{p} S_{p}}\left( \mathbb{F}_{p}, \mathbb{F}_{p}\right)\) with an A-structure such that \(\mathrm{Ext}^{\ast }_{\mathbb{F}_{p} S_{p}}\left( \mathbb{F}_{p}, \mathbb{F}_{p}\right)\) becomes a minimal model in the sense of Kadeishvili of the dg-algebra \(\mathrm{Hom}^{\ast }_{\mathbb{F}_{p} S_{p}}\left(PRes \mathbb{F}_{p}, PRes \mathbb{F}_{p}\right)\).

Keywords

A-infinity Group cohomology Symmetric group Minimal model 

Mathematics Subject Classification (2010)

18G15 

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.University of StuttgartStuttgartGermany

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