# On Singer's algebra and coalgebra structures

Bollettino dell'Unione Matematica Italiana (2006)

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

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topLomonaco, 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

top- CIAMPELLA, A. - LOMONACO, L. A., Homological computations in the universal Steenrod algebra, Preprint. Zbl1069.55014
- 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.
- LOMONACO, L. A., A phenomenon of reciprocity in the universal Steenrod algebra. Trans. Amer. Math. Soc., 330 (1992), 813-822. Zbl0745.55007
- LOMONACO, L. A., The diagonal cohomology of the universal Steenrod Algebra. J. Pure Appl. Algebra, 121 no. 3 (1997), 315-323. Zbl0891.55023
- MAY, J. P., The Steenrod algebra and its applications. Lecture Notes in Math.168, Springer, Berlin (1970), 153-231.
- SINGER, W. M., On the algebra of operations for Hopf cohomology, Bull. London Math. Soc., 37, n. 4 (2005), 627-635. Zbl1080.55014
- SINGER, W. M., Invariant theory and the Lambda algebra, Trans. Amer. Math. Soc.280 (1983), 673-693. Zbl0533.55013

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