On the set of grouplikes of a coring

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dc.creatorKaoutit, L. El
dc.creatorGomez-Torrecillas, J.
dc.date2009-01-27
dc.date.accessioned2026-07-07T12:34:55Z
dc.date.available2026-07-07T12:34:55Z
dc.descriptionWe focus our attention to the set $\gl{\coring{C}}$ of grouplike elements of a coring $\coring{C}$ over a ring $A$. We do some observations on the actions of the groups $U(A)$ and $\aut{\coring{C}}$ of units of $A$ and of automorphisms of corings of $\coring{C}$, respectively, on $\gl{\coring{C}}$, and on the subset $\galois{\coring{C}}$ of all Galois grouplike elements. Among them, we give conditions on $\coring{C}$ under which $\galois{\coring{C}}$ is a group, in such a way that there is an exact sequence of groups $\{1\} \to U(A^{g}) \to U(A) \to \galois{\coring{C}} \to \{1\},$ where $A^g$ is the subalgebra of coinvariants for some $g \in \galois{\coring{C}}$.
dc.identifierhttps://arxiv.org/abs/0901.4291
dc.identifierhttp://arxiv.org/abs/0901.4291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217610
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.titleOn the set of grouplikes of a coring
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