Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 4: 957 - 984

DOI: https://doi.org/10.1007/s11464-016-0559-2

RESEARCH ARTICLE

On duality preservability of Auslander-Reiten quivers of derived categories and cluster categories

  • Fang LI ,
  • Lingyu WAN
Expand
  • Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou 310027, China

Received date: 30 Nov 2015

Accepted date: 07 Mar 2016

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We give sufficient conditions and necessary conditions on duality preservability of Auslander-Reiten quivers of derived categories and cluster categories over hereditary algebras. Meantime, we characterize the condition of generalized path algebras as cleft extensions of path algebras.

Key words： Dual quiver; Auslander-Reiten quiver; derived category; cluster category

Cite this article

Fang LI , Lingyu WAN . On duality preservability of Auslander-Reiten quivers of derived categories and cluster categories[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 957 -984 . DOI: 10.1007/s11464-016-0559-2

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Auslander M, Reiten I, Smalo S O. Representation Theory of Artin Algebras. Cambridge Stud Adv Math, Vol 36. Cambridge: Cambridge Univ Press, 1997

2
Demonet L. Skew group algebras of path algebras and preprojective algebras. 2009, arXiv: 0902.1390

3
Happel D. Triangulated Categories in the Representation of Finite Dimensional Algebras. London Math Soc Lecture Note Ser, Vol 119. Cambridge: Cambridge Univ Press, 1988

DOI

4
Hou B, Yang S. Skew group algebras of deformed preprojective algebras. J Algebra, 2011, 332(1): 209–228

DOI

5
Hubery A W. Representations of Quivers Respecting a Quiver Automorphism and a Theorem of Kac. Ph D Thesis, The University of Leeds, 2002

6
Keller B. Cluster algebras and cluster categories. Bull Iranian Math Soc, 2011, 37: 187–234

7
Li F. Characterization of left artinian algebras through pseudo path algebras. J Aust Math Soc, 2007, 83(03): 385–416

DOI

8
Li F. Modulation and natural valued quiver of an algebra. Pacific J Math,2012, 256(1): 105–128

DOI

10
Li F, Chen L L. The natural quiver of an artinian algebra. Algebr Represent Theory, 2010, 13(5): 623–636

DOI

11
Li F, Lin Z Z. Approach to artinian algebras via natural quivers. Trans Amer Math Soc, 2012, 364(3): 1395–1411

DOI

12
Reiten I, Riedtmann C. Skew group algebras in the representation theory of artin algebras. J Algebra, 1985, 92(1): 224–282

DOI

13
Zhang M. The dual quiver of the Auslander-Reiten quiver of path algebras. Algebr Represent Theory, 2012, 15(2): 203–210

DOI

14
Zhang M, Li F. Representations of skew group algebras induced from isomorphically invariant modules over path algebras. J Algebra, 2009, 321(2): 567–581

DOI

Options
Outlines

/

〈 〉