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Spherical objects of the multiplicity free Brauer tree algebra with two edges
LIU Qunhua *
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023
*Correspondence author
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Funding: SRFDP （No.20133207120013）, NSFC （No.11671207）
Opened online: 9 July 2018
Accepted by: none
Citation: LIU Qunhua.Spherical objects of the multiplicity free Brauer tree algebra with two edges[OL]. [ 9 July 2018] http://en.paper.edu.cn/en_releasepaper/content/4745481
 
 
Spherical objects and tilting objects are important concepts in derived categories. They induce derived equivalences by taking derived tensor and mapping cone respectively. In this paper we explicitly describe, using the socalled n-complex, all spherical objects and tilting objects of the multiplicity free Brauer tree algebra with two edges. This algebra is Morita equivalent to the path algebra of a 2-cycle modulo the admissible ideal generated by the paths of length 3. We find the spherical objects are precisely the indecomposable direct summands of the tilting objects.
Keywords:Brauer tree algebra； Spherical object；tilting object；derived Picard group；n-complex
 
 
 

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