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Relations for Grothendieck groups of $n$-cluster tilting subcategories

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 نشر من قبل Alireza Nasr-Isfahani
 تاريخ النشر 2021
  مجال البحث
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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 $Lambda$.



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