Displaying similar documents to “The Auslander-Reiten quiver for posets of finite growth”

Polynomial algebra of constants of the Lotka-Volterra system

Jean Moulin Ollagnier, Andrzej Nowicki (1999)

Colloquium Mathematicae

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Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form d = x ( C y + z ) ∂ ∂ x + y ( A z + x ) ∂ ∂ y + z ( B x + y ) ∂ ∂ z , called the Lotka-Volterra derivation, where A,B,C ∈ k.

Tame three-partite subamalgams of tiled orders of polynomial growth

Daniel Simson (1999)

Colloquium Mathematicae

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Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders Λ • (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order Λ • to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders Λ • of non-polynomial growth are completely described in Theorem...

A classification of two-peak sincere posets of finite prinjective type and their sincere prinjective representations

Justyna Kosakowska (2001)

Colloquium Mathematicae

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Assume that K is an arbitrary field. Let (I, ⪯) be a two-peak poset of finite prinjective type and let KI be the incidence algebra of I. We study sincere posets I and sincere prinjective modules over KI. The complete set of all sincere two-peak posets of finite prinjective type is given in Theorem 3.1. Moreover, for each such poset I, a complete set of representatives of isomorphism classes of sincere indecomposable prinjective modules over KI is presented in Tables 8.1.

Sincere posets of finite prinjective type with three maximal elements and their sincere prinjective representations

Justyna Kosakowska (2002)

Colloquium Mathematicae

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Assume that K is an arbitrary field. Let (I,⪯) be a poset of finite prinjective type and let KI be the incidence K-algebra of I. A classification of all sincere posets of finite prinjective type with three maximal elements is given in Theorem 2.1. A complete list of such posets consisting of 90 diagrams is presented in Tables 2.2. Moreover, given any sincere poset I of finite prinjective type with three maximal elements, a complete set of pairwise non-isomorphic sincere indecomposable...

Pseudocomplemented and Stone Posets

Ivan Chajda (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.

Comparison of subset systems

Evelyn Nelson, Jiří Adámek, Andreas Jung, Jan Reiterman, Andrzej Tarlecki (1988)

Commentationes Mathematicae Universitatis Carolinae

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Indecomposable representations for extended Dynkin quivers of type 𝔼̃₈

Dawid Kędzierski, Hagen Meltzer (2011)

Colloquium Mathematicae

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We discuss the problem of classification of indecomposable representations for extended Dynkin quivers of type 𝔼̃₈, with a fixed orientation. We describe a method for an explicit determination of all indecomposable preprojective and preinjective representations for those quivers over an arbitrary field and for all indecomposable representations in case the field is algebraically closed. This method uses tilting theory and results about indecomposable modules for a canonical algebra...