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Right peak algebras of two-separate stratified posets, their Galois coverings and socle projective modules. (English) Zbl 0791.16011

Let \(k\) be a commutative field. Recall that a finite dimensional \(k\)- algebra \(R\) is called a right peak algebra if there exists a simple projective right ideal \(P_ *= e_ * R\) such that \(\text{soc}(R_ R)\) is isomorphic to a direct sum of copies of \(P_ *\). If \(R\) is a basic right peak algebra, then \(R=( {A\atop 0} {_ A M_ F \atop F})\) where \(A= (1-e_ *) R(1-e_ *)\), \(F=e_ * Re_ *\) is a division algebra and \(_ A M_ F= (1-e_ *) Re_ *\) is an \(A\)-\(F\)-bimodule which is faithful over \(A\). The aim of this paper is to study the representation type and the Auslander-Reiten quiver of the category \(\text{mod}_{\text{sp}}(R)\) of finitely generated socle projective right \(R\)-modules for a class of algebras of stratified posets introduced by the author [in Topics in algebra. Pt. I: Rings and representations of algebras, Pap. 31st Semester Class. Algebraic Struct., Warsaw/Poland 1988, Banach Cent. Publ. 26, Part 1, 499-533 (1990; Zbl 0726.16010)].

MSC:

16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16G20 Representations of quivers and partially ordered sets
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16D40 Free, projective, and flat modules and ideals in associative algebras

Citations:

Zbl 0726.16010
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