Serial coalgebras and their valued Gabriel quivers
Jos\'e G\'omez-Torrecillas, Gabriel Navarro
TL;DR
This paper investigates serial coalgebras through their valued Gabriel quivers, characterizing specific classes, describing their Auslander-Reiten quivers, and proving a related theorem about subcoalgebras.
Contribution
It introduces new characterizations of Hom-computable and representation-directed serial coalgebras and extends the Eisenbud-Griffith theorem to coalgebras.
Findings
Characterization of Hom-computable serial coalgebras
Description of Auslander-Reiten quivers for serial coalgebras
Proof that subcoalgebras of certain prime coalgebras are serial
Abstract
We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed coalgebras are characterized. The Auslander-Reiten quiver of a serial coalgebra is described. Finally, a version of Eisenbud-Griffith theorem is proved, namely, every subcoalgebra of a prime, hereditary and strictly quasi-finite coalgebra is serial.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology