Relations for Grothendieck groups of n-cluster tilting subcategories

2021/06/21 by Diyanatnezhad, Raziyeh, Nasr-Isfahani, Alireza · 1 citation
#16E20 #16G10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2106.10958

Abstract

Let Λ be an artin algebra and M be an n-cluster tilting subcategory of modΛ. We show that 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 M if and only if every effaceable functor M→ Ab has finite length. As a consequence we show that if modΛ 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 Λ.

Cited by

• Coxeter matrices and homological quadratic forms of \boldsymboln-hereditary algebras

Related

• Pure semisimple n-cluster tilting subcategories
• Grothendieck groups of repetitive cluster categories
• nℤ-Gorenstein cluster tilting subcategories
• The Grothendieck group of a triangulated category
• n-cluster tilting subcategories from gluing systems of representation-directed algebras