CHARACTERIZATION OF NAKAYAMA $m$-CLUSTER TILTED ALGEBRAS OF TYPE $A_n$

Faisal Faisal, Intan Muchtadi-Alamsyah


Abstract


Abstract. For any natural natural number m, the m-cluster tilted algebras are generalization of cluster tilted algebras. These algebras are defined as the endomorphism of certain objects in m-cluster category called m-cluster tilting objects. Finding such objectin the m-cluster category has become a combinatorial problem. In this article we charac-terize Nakayama m-cluster tilted algebras of type An by geometric description given byBaur and Marsh.

DOI : http://dx.doi.org/10.22342/jims.22.2.213.93-130


Keywords


Nakayama algebra, m-cluster tilted algebra, cluster category

References


[BM] K. Baur, R. J. Marsh, A Geometric description of m-Cluster categories, Trans. Amer. Math.Soc. 360 (2008), 5789-5803

[BMRRT] A. Buan, R. Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics, Advances in mathematics, 204 (2), 572-68(2006).

[CCS] P. Caldero, F. Chapoton, R. Schier, Quivers with relations arising from clusters (An case), Trans. Amer. Math. Soc. 358, no. 3, 1347-1364 (2006).

[FM] Faisal, I. Muchtadi-Alamsyah, On cyclic Nakayama m-cluster tilted algebra of type An, Proceeding International Conference on Mathematical Research, Education and Application, Ho Chi Minh City, 119-127 (2013).

[K] B. Keller, On triangulated orbit categories, Doc. Math. 10 (2005), 551-581.

[M] Graham J. Murphy, Derived equivalence classication of m-cluster tilted algebra of type An, Journal of Algebra (2009).

[Z] B. Zhu, Generalized cluster complexes via quiver representations, J. Algebraic Combin. 27(2008), 25-54.


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