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

Kasjan, Stanisław

Fundamenta Mathematicae, Tome 142 (1993), p. 259-279 / Harvested from The Polish Digital Mathematics Library

Résumé

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 constructed and a functorial connection between $m o d_{s p} (K I_{ϱ}^{* + \times})$ and $m o d_{s p} (K I *_{ϱ})$ is given.

Publié le : 1993-01-01

Zbl 0806.16011

EUDML-ID : urn:eudml:doc:212008

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     author = {Stanis\l aw Kasjan},
     title = {Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {259-279},
     zbl = {0806.16011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p259bwm}
}

Kasjan, Stanisław. Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations. Fundamenta Mathematicae, Tome 142 (1993) pp. 259-279. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p259bwm/

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