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

Fundamenta Mathematicae (1993)

- Volume: 143, Issue: 3, page 259-279
- ISSN: 0016-2736

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topKasjan, Stanisław. "Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations." Fundamenta Mathematicae 143.3 (1993): 259-279. <http://eudml.org/doc/212008>.

@article{Kasjan1993,

abstract = {A class of stratified posets $I*_ϱ$ is investigated and their incidence algebras $KI*_ϱ$ 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 $KI*_ϱ ≃ K(Q, Ω)$. 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 $I^\{*+×\}$ of this covering is constructed and a functorial connection between $mod_\{sp\} (KI^\{*+×\}_ϱ)$ and $mod_\{sp\}(KI*_ϱ)$ is given.},

author = {Kasjan, Stanisław},

journal = {Fundamenta Mathematicae},

keywords = {socle-projective representations; incidence algebras; stratified posets; socle-projective modules; bound quiver; universal covering; three-peak algebra; representation type; Auslander-Reiten quiver},

language = {eng},

number = {3},

pages = {259-279},

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

url = {http://eudml.org/doc/212008},

volume = {143},

year = {1993},

}

TY - JOUR

AU - Kasjan, Stanisław

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

JO - Fundamenta Mathematicae

PY - 1993

VL - 143

IS - 3

SP - 259

EP - 279

AB - A class of stratified posets $I*_ϱ$ is investigated and their incidence algebras $KI*_ϱ$ 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 $KI*_ϱ ≃ K(Q, Ω)$. 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 $I^{*+×}$ of this covering is constructed and a functorial connection between $mod_{sp} (KI^{*+×}_ϱ)$ and $mod_{sp}(KI*_ϱ)$ is given.

LA - eng

KW - socle-projective representations; incidence algebras; stratified posets; socle-projective modules; bound quiver; universal covering; three-peak algebra; representation type; Auslander-Reiten quiver

UR - http://eudml.org/doc/212008

ER -

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