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## Fundamenta Mathematicae

1993 | 143 | 3 | 259-279
Tytuł artykułu

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

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
259-279
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-11-16
poprawiono
1993-03-29
Twórcy
autor
• Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
• [AS] I. Assem and A. Skowroński, On some class of simply connected algebras, Proc. London Math. Soc. 56 (1988), 417-450.
• [Ga] P. Gabriel, The universal cover of a representation finite algebra, in: Lecture Notes in Math. 903, Springer, 1981, 68-105.
• [Gr] E. L. Green, Group graded algebras and the zero relation problem, in: Lecture Notes in Math. 903, Springer, 1981, 106-115.
• [MP] R. Martínez-Villa and J. A. de la Pe na, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (1983), 277-292.
• [S1] D. Simson, On the representation type of stratified posets, C. R. Acad. Sci. Paris 311 (1990), 5-10.
• [S2] D. Simson, Representations of bounded stratified posets, coverings and socle projective modules, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa, 1990, 499-533.
• [S3] D. Simson, A splitting theorem for multipeak path algebras, Fund. Math. 138 (1991), 113-137.
• [S4] D. Simson, Right peak algebras of two-separate stratified posets, their Galois covering and socle projective modules, Comm. Algebra 20 (1992), 3541-3591.
• [S5] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic Appl. 4, Gordon & Breach, 1992.
• [Sp] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
• [W] Th. Weichert, Darstellungstheorie von Algebren mit projektivem Sockel, Doctoral Thesis, Universität Stuttgart, 1989.
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Bibliografia
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