On Singer's algebra and coalgebra structures
Lomonaco, Luciano A.
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 611-617 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Recentemente W. M. Singer ha introdotto le nozioni di algebra con coprodotti e di coalgebra con prodotti, indebolendo, in un certo senso, la nozione di algebra di Hopf (cfr [6]). Nel presente lavoro si considerano alcune particolari algebre di invarianti e si dimostra che esse costituiscono infatti ulteriori esempi di algebre con coprodotti e di coalgebre con prodotti. Si discute inoltre la stretta relazione fra tali algebre e le strutture considerate da W. M. Singer, fornendo, in particolare, una descrizione di queste ultime in termini di invarianti modulari.

Publié le : 2006-10-01
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     author = {Luciano A. Lomonaco},
     title = {On Singer's algebra and coalgebra structures},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {611-617},
     zbl = {1177.55010},
     mrnumber = {2274115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_3_611_0}
}

Lomonaco, Luciano A. On Singer's algebra and coalgebra structures. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 611-617. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_3_611_0/

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