Room 515, Cosmology Bldg., National Taiwan University + Zoom, Online + Onsite Course
(實體+線上課程 台灣大學次震宇宙館515研討室+ Zoom)
Length of Triangulated Categories
Yuki Hirano (Tokyo University of Agriculture and Technology)
Abstract
Composition series is fundamental in the study of finite groups and finite dimensional modules.
One of the most important properties of such composition series is the Jordan-Hölder property, and this implies the property that all composition series have the same length (we call this the Jordan--Dedekind property).
In this talk, I will introduce the notion of composition series for triangulated categories, and discuss composition series of derived categories of certain finite dimensional algebras and smooth projective varieties. In particular, I will explain that the Jordan--Dedekind property does not hold for derived categories of certain finite dimensional algebras of finite global dimension and certain smooth projective toric surfaces. This talk is based on joint work with Kalck and Ouchi.
Organizer: Pedro Núñez (NTU)
