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Let $Lambda$ be an artin algebra and $mathcal{M}$ be an n-cluster tilting subcategory of mod$Lambda$. We show that $mathcal{M}$ has an additive generator if and only if the n-almost split sequences form a basis for the relations for the Grothendieck group of $mathcal{M}$ if and only if every effaceable functor $mathcal{M}rightarrow Ab$ has finite length. As a consequence we show that if mod$Lambda$ has n-cluster tilting subcategory of finite type then the n-almost split sequences form a basis for the relations for the Grothendieck group of $Lambda$.
Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement $(mathcal A ,mathcal B,mathcal C)$ of
Let $mathscr C$ be a Krull-Schmidt $(n+2)$-angulated category and $mathscr A$ be an $n$-extension closed subcategory of $mathscr C$. Then $mathscr A$ has the structure of an $n$-exangulated category in the sense of Herschend-Liu-Nakaoka. This constru
In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of
APR tilts for path algebra $kQ$ can be realized as the mutation of the quiver $Q$ in $mathbb Z Q$ with respect to the translation. In this paper, we show that we have similar results for the quadratic dual of truncations of $n$-translation algebras,
In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this $d$-cluster category.