Monomorphisms of coalgebras

• Autorzy: A. L. Agore
• Języki publikacji: EN

Abstrakty

EN

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 $∑_{i∈I} ε(a^{i}) b^{i} = ∑_{i∈I} a^{i} ε(b^{i})$ for all $∑_{i∈I} a^{i}⊗ b^{i} ∈ C ◻_{D} C$. In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.

Kategorie tematyczne

• 16T15: Coalgebras and comodules; corings
• 16T05: Hopf algebras and their applications

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 120
• Numer: 1
• Strony: 149-155

Daty

wydano

2010

Twórcy

autor

A. L. Agore

• Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, RO-010014 Bucureşti 1, Romania
• Department of Mathematics, Academy of Economic Studies, Piata Romana 6, RO-010374 Bucureşti 1, Romania

Identyfikatory

DOI

10.4064/cm120-1-11