Tokyo-Nagoya Algebra Seminar

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Organizer(s) Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi

2020/10/27

16:30-18:00   Online
Please see the URL below for details on the online seminar.
Yasuaki Gyoda (Nagoya University)
Positive cluster complex and $\tau$-tilting complex (Japanese)
[ Abstract ]
In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.