A note on the algebra of operations for Hopf cohomology at odd primes

  • Maurizio Brunetti
  • Adriana Ciampella
  • Luciano A. Lomonaco
Article

Abstract

Let p be any prime, and let \({\mathcal B}(p)\) be the algebra of operations on the cohomology ring of any cocommutative \(\mathbb {F}_p\)-Hopf algebra. In this paper we show that when p is odd (and unlike the \(p=2\) case), \({\mathcal B}(p)\) cannot become an object in the Singer category of \(\mathbb {F}_p\)-algebras with coproducts, if we require that coproducts act on the generators of \({\mathcal B}(p)\) coherently with their nature of cohomology operations.

Keywords

Steenrod algebra Cohomology operations Hopf algebras 

Mathematics Subject Classification

55S10 55T15 

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Copyright information

© Università degli Studi di Napoli "Federico II" 2017

Authors and Affiliations

  • Maurizio Brunetti
    • 1
  • Adriana Ciampella
    • 1
  • Luciano A. Lomonaco
    • 1
  1. 1.Department of Mathematics and ApplicationsUniversity of Naples “Federico II”NaplesItaly

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