Recollements of Quiver Representations Induced by Evaluation Functors  

作　　者：Yu Zhang Huanhuan Li Yuefei Zheng 

机构地区：[1]College of Science,Northwest A&F University,Yangling,Shaanxi 712100,China [2]School of Mathematics and Statistics,Xidian University,Xi'an 710071,China

出　　处：《Algebra Colloquium》2024年第4期609-628,共20页代数集刊（英文版）

基　　金：NSFC(Grant Nos.11701455 and 12101474);Fundamental Research Funds for the Central Universities(Grant No.2452020182).

摘　　要：Let Q=(Qo,Qi)be an arbitrary acyclic quiver and M an abelian category satisfying AB3 and AB3*.Let Rep(Q,M)be the category of M-valued representations of Q and Rep;(Q,M)its full subcategory consisting of representations with 0 at vertex i.We construct a recollement of Rep(Q,M)by Rep;(Q,M)and M.If in addition,M has enough projective and injective objects,and satisfies AB4 and AB4*,then this recollement can be lifted to the derived levels.In the case that Q is finite and M is the module category Mod A over some finite dimensional algebra A,we give several direct applications concerning the relationship between homological properties of A and AQ.In particular,we find that the Cartan determinant conjecture always holds true for AQ with IQolanevennumber.

关 键 词：quiver representations abelian categories recollements derived recollements homological properties 

分 类 号：O174[理学—数学]