# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

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

### Tom 143 / 1993

Fundamenta Mathematicae 143 (1993), 259-279 DOI: 10.4064/fm-143-3-259-279

#### Streszczenie

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.

#### Autorzy

• Stanisław KasjanInstitute of Mathematics
Nicholas Copernicus University
Chopina 12/18
87-100 Toruń, Poland

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