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Subjects
16-XX Associative rings and algebras
16Gxx Representation theory of rings and algebras
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

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Displaying 1 – 2 of 2

Bipartite coalgebras and a reduction functor for coradical square complete coalgebras

Justyna Kosakowska, Daniel Simson (2008)

Colloquium Mathematicae

Let C be a coalgebra over an arbitrary field K. We show that the study of the category C-Comod of left C-comodules reduces to the study of the category of (co)representations of a certain bicomodule, in case C is a bipartite coalgebra or a coradical square complete coalgebra, that is, C = C₁, the second term of the coradical filtration of C. If C = C₁, we associate with C a K-linear functor $ℍ_{C} : C - C o m o d \to H_{C} - C o m o d$ that restricts to a representation equivalence $ℍ_{C} : C - c o m o d \to H_{C} - c o m o d_{s p}^{•}$ , where $H_{C}$ is a coradical square complete hereditary bipartite...

Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations

Stanisław Kasjan (1993)

Fundamenta Mathematicae

A class of stratified posets $I *_{ϱ}$ is investigated and their incidence algebras $K I *_{ϱ}$ are studied in connection with a class of non-shurian vector space categories. Under some assumptions on $I *_{ϱ}$ we associate with $I *_{ϱ}$ a bound quiver (Q, Ω) in such a way that $K I *_{ϱ} ≃ K (Q, Ω)$ . We show that the fundamental group of (Q, Ω) is the free group with two free generators if $I *_{ϱ}$ is rib-convex. In this case the universal Galois covering of (Q, Ω) is described. If in addition $I_{ϱ}$ is three-partite a fundamental domain $I^{* + \times}$ of this covering is...

Currently displaying 1 – 2 of 2

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