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

Faisal Faisal; Intan Muchtadi-Alamsyah

doi:10.22342/jims.22.2.213.93-130

Faisal Faisal ⁽¹⁾ , Intan Muchtadi-Alamsyah ⁽²⁾

(1) Institut Teknologi Bandung,

(2) Institut Teknologi Bandung

https://doi.org/10.22342/jims.22.2.213.93-130

Issue
Volume 22 Number 2 (October 2016)

Submitted
April 27, 2015

Accepted
August 7, 2016

Published
October 24, 2016

Keywords:

Nakayama algebra, m-cluster tilted algebra, cluster category

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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

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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.

Authors

Faisal Faisal

Institut Teknologi Bandung

Intan Muchtadi-Alamsyah

Institut Teknologi Bandung

ntan@math.itb.ac.id (Primary Contact)

Faisal, F., & Muchtadi-Alamsyah, I. (2016). CHARACTERIZATION OF NAKAYAMA $m$-CLUSTER TILTED ALGEBRAS OF TYPE $A_n$. Journal of the Indonesian Mathematical Society, 22(2), 93–130. https://doi.org/10.22342/jims.22.2.213.93-130