The aim of this paper is to introduce τ-tilting theory, which 'completes'(classical) tilting theory
from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting …

We introduce a new category C, which we call the cluster category, obtained as a quotient of
the bounded derived category D of the module category of a finite-dimensional hereditary …

References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from
representation theory of finite-dimensional algebras. Recently these higher analogues of …

In this paper, we study τ-tilting modules over Nakayama algebras. We establish bijections
between τ-tilting modules, triangulations of a polygon with a puncture, and certain integer …

Abstract In 1996, Edelman and Reiner defined the two higher Stasheff–Tamari orders on
triangulations of cyclic polytopes and conjectured them to coincide. We open up an …

However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

For a left noetherian ring, we establish a bijective correspondence between equivalence
classes of cotilting-modules which are not necessarily finitely generated, and torsion pairs …

We classify the torsion pairs in a tube category and show that they are in bijection with
maximal rigid objects in the extension of the tube category containing the Prüfer and adic …