The weak braided Hopf algebra structure of some Cayley–Dickson algebras |
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Authors: | Daniel Bulacu |
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Affiliation: | aFaculty of Mathematics and Informatics, University of Bucharest, Str. Academiei 14, RO-010014 Bucharest 1, Romania |
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Abstract: | It has been shown by Albuquerque and Majid that a class of unital k-algebras, not necessarily associative, obtained through the Cayley–Dickson process can be viewed as commutative associative algebras in some suitable symmetric monoidal categories. In this note we will prove that they are, moreover, commutative and cocommutative weak braided Hopf algebras within these categories. To this end we first define a Cayley–Dickson process for coalgebras. We then see that the k-vector space of complex numbers, of quaternions, of octonions, of sedenions, etc. fit to our theory, hence they are all monoidal coalgebras as well, and therefore weak braided Hopf algebras. |
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Keywords: | Quasialgebra Quasicoalgebra Cayley– Dickson weak braided Hopf algebra |
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