Geodesic
COALTERNATIVE COALGEBRAS
Glasgow mathematical journal, Tome 62 (2020), pp. S142-S164

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we define a Cayley–Dickson process for k-coalgebras proving some results that describe the properties of the final coalgebra, knowing the properties of the initial one. Namely, after applying the Cayley–Dickson process for k-coalgebras to a coassociative coalgebra, we obtain a coalternative one. Moreover, the first coalgebra is cocommutative if and only if the final coalgebra is coassociative. Finally we extend these results to a more general approach of D-coalgebras, where D is a k-coalgebra, presenting a class of examples of coalternative (non-coassociative) coalgebras obtained from group D-coalgebras. 
ALBUQUERQUE, HELENA; BARREIRO, ELISABETE; SÁNCHEZ, JOSÉ M.; CALVO, CARLOS SONEIRA. COALTERNATIVE COALGEBRAS. Glasgow mathematical journal, Tome 62 (2020), pp. S142-S164. doi: 10.1017/S0017089519000314
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     author = {ALBUQUERQUE, HELENA and BARREIRO, ELISABETE and S\'ANCHEZ, JOS\'E M. and CALVO, CARLOS SONEIRA},
     title = {COALTERNATIVE {COALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {S142--S164},
     year = {2020},
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     number = {S1},
     doi = {10.1017/S0017089519000314},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000314/}
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