We define a dimension for a triangulated category. We prove a representability Theorem for
a class of functors on finite dimensional triangulated categories. We study the dimension of …

We introduce the concept of maximal (n− 1)-orthogonal subcategories over Artin algebras
and orders, and develop (n+ 1)-dimensional Auslander–Reiten theory on them. We give the …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

We find a simple condition which implies finiteness of finitistic global dimension for artin
algebras. As a consequence we obtain a short proof of the finitistic global dimension …

Abstract We introduce (n+ 1)-preprojective algebras of algebras of global dimension n. We
show that if an algebra is n-representation-finite then its (n+ 1)-preprojective algebra is self …

In topological data analysis, two-parameter persistence can be studied using the
representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of …

We determine the representation dimension of exterior algebras. This provides the first
known examples of representation dimension> 3. We deduce that the Loewy length of the …

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over
fields and orders over complete local rings. Then we introduce $ n $-cluster tilting …

We discuss applications of exact structures and relative homological algebra to the study of
invariants of multiparameter persistence modules. This paper is mostly expository, but does …

The associated strangeness production in pp collisions was studied at bombarding energies
of 2.3 and 2.7 GeV by detecting the outgoing K+ particles with a high resolution magnetic …