The class of support-tilting modules was introduced to provide a completion of the class of
tilting modules from the point of view of mutations. In this article, we study-tilting finite …

We introduce the new concept of silting modules. These modules generalize tilting modules
over an arbitrary ring, as well as support-tilting modules over a finite dimensional algebra …

The class of support-tilting modules was introduced recently by Adachi et al. These modules
complete the class of tilting modules from the point of view of mutations. Given a finite …

We study two kinds of reduction processes of triangulated categories, that is, silting
reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal …

The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters.
Through the recent" categorifications" of cluster algebras using representation theory one …

Derived equivalences and t-structures are closely related. We use realisation functors
associated to t-structures in triangulated categories to establish a derived Morita theory for …

In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …

We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting
complexes by giving a bijection between tilting complexes and the braid group of the …