We generalise $\tau $-cluster morphism categories to non-positive proper dg algebras. The
compatibility of silting reduction with support $\tau $-tilting reduction will be an essential …

Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …

Building on work of Jasso, we prove that any projectively generated $ d $-abelian category
is equivalent to a $ d $-cluster tilting subcategory of an abelian category with enough …

We build foundations of an approach to study canonical forms of $2 $-Calabi--Yau
triangulated categories with cluster-tilting objects, using dg algebras and relative singularity …

We generalize the notions of $ d $-cluster tilting pair and $ d $-Auslander exact dg category
to $ d $-precluster tilting triple and $ d $-minimal Auslander--Gorenstein exact dg category …

arXiv:1012.6014v1 [math.RT] 29 Dec 2010 Page 1 arXiv:1012.6014v1 [math.RT] 29 Dec 2010
TILTING THEORY AND CLUSTER ALGEBRAS IDUN REITEN Introduction The purpose of this …

Given a negatively graded Calabi-Yau algebra, we regard it as a DG algebra with vanishing
differentials and study its cluster category. We show that this DG algebra is sign-twisted …

Given n≤ d<∞ n≦d<∞, we investigate the existence of algebras of global dimension d
which admit an n-cluster tilting subcategory. We construct many such examples using …

Let $\mathcal {A} $ be an abelian length category containing a $ d $-cluster tilting
subcategory $\mathcal {M} $. We prove that a subcategory of $\mathcal {M} $ is a $ d …

Let\cal M ℳ be an n-cluster tilting subcategory of mod-Λ, where Λ is an Artin algebra. Let\cal
S (\cal M) S (ℳ) denote the full subcategory of\cal S (Λ) S (Λ), the submodule category of Λ …