Details

Autor(en) / Beteiligte

• Asadollahi, Javad
• Hafezi, Rasool
• Sadeghi, Somayeh

Titel

On the monomorphism category of n-cluster tilting subcategories

Ist Teil von

• Science China. Mathematics, 2022-07, Vol.65 (7), p.1343-1362

Ort / Verlag

Beijing: Science China Press

Erscheinungsjahr

2022

Link zum Volltext

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• Let ℳ be an n -cluster tilting subcategory of mod-Λ, where Λ is an Artin algebra. Let S ( ℳ ) denote the full subcategory of S ( Λ ) , the submodule category of Λ, consisting of all the monomorphisms in ℳ . We construct two functors from S ( ℳ ) to mod − ℳ ¯ , the category of finitely presented additive contravariant functors on the stable category of ℳ . We show that these functors are full, dense and objective and hence provide equivalences between the quotient categories of S ( ℳ ) and mod − ℳ ¯ . We also compare these two functors and show that they differ by the n -th syzygy functor, provided ℳ is an n ℤ-cluster tilting subcategory. These functors can be considered as higher versions of the two functors studied by Ringel and Zhang (2014) in the case Λ = k [ x ] / 〈 x n 〉 and generalized later by Eiríksson (2017) to self-injective Artin algebras. Several applications are provided.