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2013•Journal of Mathematical and Fundamental SciencesOpen access

Auslander Reiten Quiver of Nakayama Algebra type Dynkin Graph An

Faisal Faisal, Irawati Irawati, Intan Muchtadi-Alamsyah

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Abstract

In this paper we will determine Auslander Reiten quiver of Nakayama algebra with quiver type Dynkin graph A n for all natural number n ≥ 2. The ARquiver is a visualization of module category of finite dimensional algebras.From the AR-quiver of an algebra A we may know all the isomorphism classes of indecomposable modules in mod A and the homomorphism between them.Once we get the general shape of the AR-quiver of this algebra, we will use it to compute a tilting module of this algebra.

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What this paper is about

In this paper we will determine Auslander Reiten quiver of Nakayama algebra with quiver type Dynkin graph A n for all natural number n ≥ 2. The ARquiver is a visualization of module category of finite dimensional algebras.From the AR-quiver of an algebra A we may know all the isomorphism classes of indecomposable modules in mod A and the homomorphism between them.Once we get the general shape of the AR-quiver of this algebra, we will use it to compute a tilting module of this algebra.

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Available abstract

In this paper we will determine Auslander Reiten quiver of Nakayama algebra with quiver type Dynkin graph A n for all natural number n ≥ 2. The ARquiver is a visualization of module category of finite dimensional algebras.From the AR-quiver of an algebra A we may know all the isomorphism classes of indecomposable modules in mod A and the homomorphism between them.Once we get the general shape of the AR-quiver of this algebra, we will use it to compute a tilting module of this algebra.

Key concepts: Quiver, Mathematics, Indecomposable module, Pure mathematics, Isomorphism (crystallography), Algebra over a field, Graph algebra, Type (biology)

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