| 研究実績の概要 |
The research during this year has proceeded in two main directions. The first direction is the investigation of n-cluster-tilting in derived categories of algebras of finite global dimension, using the concept of silting. Here, the notion of an orbital n-cluster-tilting subcategory has been generalised using silting, giving a tool to understand a large class of n-cluster-tilting subcategories of derived categories in a unified framework. The question arises which n-cluster-tilting subcategories of derived categories arise as such generalised orbital subcategories.
Related to this, some work was also done to clarify the connection between local boundedness in the module category respectively the stable module categories of a locally bounded k-linear category.
The second direction is the investigation of functors between cluster categories of Dynkin type that was initiated in 2018. Here, some preliminary results have been obtained in the direction of extending the existing results for Dynkin type A to Dynkin type D. The main idea has been to transport results from type A to type D, by writing algebras of type D as skew-group algebras of algebras of type A, and using the resulting adjunction between the derived categories of the respective algebras to carry over the results.
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