JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 74-76.doi: 10.6040/j.issn.1671-9352.0.2019.388

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Number of tilting modules over a class of Auslander algebras

ZAN Li-bo1, ZHANG Xiao-jin2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China
  • Published:2020-04-09

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Abstract: For a radical square zero algebra B of type An, the number of tilting modules over the Auslander algebra of B is 2n-1.

Key words: Auslander algebra, radical square zero algebra, tilting module

CLC Number: 

  • O154.2
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[2] AUSLANDER M, REITEN I, SMALO S O. Representation theory of Artin algebras[C] //Cambridge Studies in Advanced Mathematics, 36. Cambridge: Cambridge University Press, 1997.
[3] BRUSTLE T, HILLE L, RINGEL C M, et al. The Δ-filtered modules without self-extensions for the Auslander algebra of K[x] /(xn)[J]. Algebra Representation Theory, 1999, 2:295-312.
[4] KAJITA N. The number of tilting modules over hereditary algebras and tilting modules over Auslander algebras[D]. Nagoya: Nagoya University, 2008.
[5] ADACHI T, IYAMA O, REITEN I. τ-tilting theory [J]. Compositio Mathematica, 2014, 150:415-452.
[6] IYAMA O, ZHANG X J. Classifying τ-tilting modules over the Auslander algebra of K[x] /(xn)[J]. Journal of the Mathematical Society of Japan, http://arxiv.org/abs/1602.05037.
[7] IYAMA O, ZHANG X J. Tilting modules over Auslander-Gorenstein algebras[J]. Pacific Journal of Mathematics, 2019, 298(2):399-416.
[1] CHEN Wen-qian, ZHANG Xiao-jin, ZAN Li-bo. The number of tilting modules over Gorenstein algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 14-16.
[2] SUN Wei-kun, LIN Han-xing. Representation dimension of one-point extension algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 85-91.
[3] LEI Xue-ping. Almost complete C-tilting modules [J]. J4, 2011, 46(2): 101-104.
[4] . AuslanderReiten correspondence for WCtilting modules [J]. J4, 2009, 44(12): 41-43.
[5] LEI Xue-ping . W-C-tilting modules [J]. J4, 2008, 43(10): 27-30 .
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