Monomorphisms of coalgebras

A. L. Agore

A. L. Agore

Colloquium Mathematicae, Tome 120 (2010), p. 149-155 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if $\sum_{i \in I} ε (a^{i}) b^{i} = \sum_{i \in I} a^{i} ε (b^{i})$ for all $\sum_{i \in I} a^{i} \otimes b^{i} \in C ◻_{D} C$ . In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.

Publié le : 2010-01-01

Zbl 1196.16031

EUDML-ID : urn:eudml:doc:284052

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     author = {A. L. Agore},
     title = {Monomorphisms of coalgebras},
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {149-155},
     zbl = {1196.16031},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-11}
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A. L. Agore. Monomorphisms of coalgebras. Colloquium Mathematicae, Tome 120 (2010) pp. 149-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-1-11/