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COALTERNATIVE COALGEBRAS

Part of: Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  20 August 2019

HELENA ALBUQUERQUE ,
ELISABETE BARREIRO ,
JOSÉ M. SÁNCHEZ  and
CARLOS SONEIRA CALVO
HELENA ALBUQUERQUE
Affiliation:
CMUC, Department of Mathematics, University of Coimbra Apartado 3008, 3001-454 Coimbra, Portugal e-mail: lena@mat.uc.pt, mefb@mat.uc.pt, txema.sanchez@mat.uc.pt
ELISABETE BARREIRO
Affiliation:
CMUC, Department of Mathematics, University of Coimbra Apartado 3008, 3001-454 Coimbra, Portugal e-mail: lena@mat.uc.pt, mefb@mat.uc.pt, txema.sanchez@mat.uc.pt
JOSÉ M. SÁNCHEZ
Affiliation:
CMUC, Department of Mathematics, University of Coimbra Apartado 3008, 3001-454 Coimbra, Portugal e-mail: lena@mat.uc.pt, mefb@mat.uc.pt, txema.sanchez@mat.uc.pt
CARLOS SONEIRA CALVO
Affiliation:
Department of Pedagogy and Didactics A Coruña, University of A Coruña, Spain e-mail: carlos.soneira@udc.gal
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Abstract

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.

MSC classification

Primary: 16T15: Coalgebras and comodules; corings
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S142 - S164
Copyright
© Glasgow Mathematical Journal Trust 2019

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References

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