اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRelations for Grothendieck groups of $n$-cluster tilting subcategories
111
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 $Lambda$.
قيم البحث
اقرأ أيضاً
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
extriangulated categories, we show that $n$-tilting (resp. $n$-cotilting) subcategories in $mathcal A$ and $mathcal C$ can be glued to get $n$-tilting (resp. $n$-cotilting) subcategories in $mathcal B$ under certain conditions.
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
ction gives $n$-exangulated categories which are not $n$-exact categories in the sense of Jasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann in general. As an application, our result can lead to a recent main result of Klapproth.
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
cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite dimensional symmetric and satisfy $tau^2=id$. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities.
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,
that is, under certain condition, the $n$-APR tilts of such algebras are realized as $tau$-mutations.For the dual $tau$-slice algebras with bound quiver $Q^{perp}$, we show that their iterated $n$-APR tilts are realized by the iterated $tau$-mutations in $mathbb Z|{n-1}Q^{perp}$.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
