On Singer's algebra and coalgebra structures

Luciano A. Lomonaco

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 611-617
  • ISSN: 0392-4041

Abstract

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Recently W. M. Singer has introduced the notion of algebra with coproducts (and the dual notion of coalgebra with products) by somehow weakening the notion of Hopf algebra (see [6]). In this paper we consider certain algebras of invariants and show that they are, in fact, further examples of algebras with coproducts and coalgebras with products. Moreover, we discuss the close relation between such algebras and the structures considered in Singer's paper.

How to cite

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Lomonaco, Luciano A.. "On Singer's algebra and coalgebra structures." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 611-617. <http://eudml.org/doc/289626>.

@article{Lomonaco2006,
abstract = {Recently W. M. Singer has introduced the notion of algebra with coproducts (and the dual notion of coalgebra with products) by somehow weakening the notion of Hopf algebra (see [6]). In this paper we consider certain algebras of invariants and show that they are, in fact, further examples of algebras with coproducts and coalgebras with products. Moreover, we discuss the close relation between such algebras and the structures considered in Singer's paper.},
author = {Lomonaco, Luciano A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {611-617},
publisher = {Unione Matematica Italiana},
title = {On Singer's algebra and coalgebra structures},
url = {http://eudml.org/doc/289626},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Lomonaco, Luciano A.
TI - On Singer's algebra and coalgebra structures
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 611
EP - 617
AB - Recently W. M. Singer has introduced the notion of algebra with coproducts (and the dual notion of coalgebra with products) by somehow weakening the notion of Hopf algebra (see [6]). In this paper we consider certain algebras of invariants and show that they are, in fact, further examples of algebras with coproducts and coalgebras with products. Moreover, we discuss the close relation between such algebras and the structures considered in Singer's paper.
LA - eng
UR - http://eudml.org/doc/289626
ER -

References

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  1. CIAMPELLA, A. - LOMONACO, L. A., Homological computations in the universal Steenrod algebra, Preprint. Zbl1069.55014
  2. LOMONACO, L. A., Dickson invariants and the universal Steenrod algebra. Topology, Proc. 4th Meet., Sorrento/Italy 1988, Suppl. Rend. Circ. Mat. Palermo, II. Ser., 24 (1990), 429-443. 
  3. LOMONACO, L. A., A phenomenon of reciprocity in the universal Steenrod algebra. Trans. Amer. Math. Soc., 330 (1992), 813-822. Zbl0745.55007
  4. LOMONACO, L. A., The diagonal cohomology of the universal Steenrod Algebra. J. Pure Appl. Algebra, 121 no. 3 (1997), 315-323. Zbl0891.55023
  5. MAY, J. P., The Steenrod algebra and its applications. Lecture Notes in Math.168, Springer, Berlin (1970), 153-231. 
  6. SINGER, W. M., On the algebra of operations for Hopf cohomology, Bull. London Math. Soc., 37, n. 4 (2005), 627-635. Zbl1080.55014
  7. SINGER, W. M., Invariant theory and the Lambda algebra, Trans. Amer. Math. Soc.280 (1983), 673-693. Zbl0533.55013

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