math.RA

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# Title: On the set of grouplikes of a coring

Abstract: We 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 $g \in \galois{\coring{C}}$.
 Subjects: Rings and Algebras (math.RA); Quantum Algebra (math.QA) Cite as: arXiv:0901.4291 [math.RA] (or arXiv:0901.4291v1 [math.RA] for this version)

## Submission history

From: EL Kaoutit Laiachi [view email]
[v1] Tue, 27 Jan 2009 17:33:43 GMT (13kb)
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