Auslander Reiten Quiver of Nakayama Algebra type Dynkin Graph An
DOI:
https://doi.org/10.5614/j.math.fund.sci.2013.45.1.1Keywords:
AR-quiver, Nakayama algebra, quiver, Dynkin type A.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.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.
Auslander, M., Reiten, I. & Smalo, S.O., Representation Theory of Artin Algebras, Cambridge University Press, 1995.
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.
Bernstein, I.N., Gelfand, I.M. & Ponomarev, V.A., Coxeter Functors and Gabriel's Theorem, Uspiehi Mat. Nauk, 28, pp. 19-33, 1973 (in Russian), English translation in Russian Math. Surveys, 28, pp. 17-32, 1973.
Hugel, L.A., Happel, D. & Krause, H., Handbook of Tilting Theory, Cambridge University Press, 2008.
