The Cartan Matrix of a Centralizer Algebra

Proceedings Mathematical Sciences

Amritanshu Prasad¹  Umesh V Dubey³  Pooja Singla² 

[1] Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva 0, Israel$$;$$;The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 00 , India$$

关键词: Centralizer algebras;    Cartan matrix;    global dimension.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices. With the help of our Cartan matrix calculations we determine their global dimensions. Many of these algebras are of infinite global dimension.

【 授权许可】

Unknown