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Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 463–476 | Cite as

An Example in the Singer Category of Algebras with Coproducts at Odd Primes

  • Maurizio BrunettiEmail author
  • Adriana Ciampella
  • Luciano A. Lomonaco
Article

Abstract

In 2005, William M. Singer introduced the notion of k-algebra with coproducts for any commutative ring k and showed that the algebra of operations on the cohomology ring of any cocommutative \(\mathbb {F}_{2}\)-Hopf algebra can be endowed with such structure. In this paper, we show that the same is true when the ground field of the cocommutative Hopf algebra is \(\mathbb {F}_{p}\), p is any odd prime, and the algebra of operations \({\mathcal {B}}(p)\) is equipped with an exotic coproduct. We also give an explicit description of the coalgebra with products dual to \({\mathcal {B}} (p)\).

Keywords

Steenrod algebra Algebras with coproducts Hopf algebras 

Mathematics Subject Classification (2010)

55S10 16T15 

Notes

Acknowledgments

The authors would like the anonymous referees who carefully read the paper and suggested some improvements, and professor Nguyen Huu Viet Hung from Department of Mathematics, Vietnam National University, Hanoi. Some ideas in this paper were developed after his visit at University of Naples.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

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

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