Auslander Reiten Quiver of Nakayama Algebra type Dynkin Graph An

Faisal Anwar, I. Irawati, Intan Muchtadi-Alamsyah

Abstract


In this paper we will determine Auslander Reiten quiver of Nakayama algebra with quiver type Dynkin graph An for all natural number n ≥ 2. The AR-quiver 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.

Keywords


AR-quiver; Nakayama algebra; quiver; Dynkin type A.

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References


Auslander, M., Representation Theory of Artin Algebras II, Comm. Algebra, 1, pp. 269¬-310, 1974.

Auslander, M., Representation Theory of Artin Algebras III, Comm. Algebra, 3, pp. 269¬-310, 1975.

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Assem, I., Simson, D. & Skowronski, A., Elements of the Representation Theory of Associative Algebras, Cambridge University Press, 2006.

Auslander, M., Platzeck, M.I. & Reiten, I., Coxeter Functors without Diagrams, Trans. Amer. Math. Soc., 250, pp. 1-46, 1979.

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Hugel, L.A., Happel, D. & Krause, H., Handbook of Tilting Theory, Cambridge University Press, 2008.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2013.45.1.1

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