| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
The structure of the derived category over a finite dimensional algebra was investigated from the viewpoint of tilting mutation theory and derived equivalences. In particular, the tilting-discreteness of a given algebra was studied, and a powerful method of showing the tilting-discreteness was given. This leads to the following results: (1) any preprojective algebra of Dynkin type is tilting-discrete. (2) a Brauer graph algebra is tilting-discrete if and only if the Brauer graph has at most one odd-cycle and none of even-cycle.
Moreover, it was proved that the Bongartz completion for presilting objects is possible in a silting-discrete triangulated category.
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