Tokyo-Nagoya Algebra Seminar

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Organizer(s) Noriyuki Abe, Aaron Chan, Erik Darpoe, Osamu Iyama, Tsutomu Nakamura, Hiroyuki Nakaoka, Ryo Takahashi

2022/01/21

16:45-18:15   Online
Please see the URL below for details on the online seminar.
Haruhisa Enomoto (Osaka Prefecture University)
Exact-categorical properties of subcategories of abelian categories 2 (Japanese)
[ Abstract ]
Quillen's exact category is a powerful framework for studying extension-closed subcategories of abelian categories, and provides many interesting questions on such subcategories.
In the first talk, I will explain the basics of some properties and invariants of exact categories (e.g. the Jordan-Holder property, simple objects, and Grothendieck monoid).
In the second talk, I will give some results and questions about particular classes of exact categories arising in the representation theory of algebras (e.g. torsion(-free) classes over path algebras and preprojective algebras).
If time permits, I will discuss questions of whether these results can be generalized to extriangulated categories (extension-closed subcategories of triangulated categories).
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html