Indices and c-vectors in extriangulated categories  

作　　者：Li Wang Jiaqun Wei Haicheng Zhang 

机构地区：[1]School of Mathematics-Physics and Finace,Anhui Polytechnic University,Wuhu 241000,China [2]Institute of Mathematics,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China

出　　处：《Science China Mathematics》2023年第9期1949-1964,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12271257)。

摘　　要：Let C be an extriangulated category and T be any n-cluster tilting subcategory of C.We consider the index with respect to T and introduce the index Grothendieck group of T.Using the index,we prove that the index Grothendieck group of T is isomorphic to the Grothendieck group of C,which implies that the index Grothendieck groups of any two n-cluster tilting subcategories are isomorphic.In particular,we show that the split Grothendieck groups of any two 2-cluster tilting subcategories are isomorphic.Then we develop a general framework for c-vectors of 2-Calabi-Yau extriangulated categories with respect to arbitrary 2-cluster tilting subcategories.We show that the c-vectors have the sign-coherence property and provide some formulas for calculating c-vectors.

关 键 词：extriangulated categories cluster tilting subcategories indices c-vectors 

分 类 号：O154.1[理学—数学]