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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/122/01/0067-0073

    • Keywords

       

      Centralizer algebras; Cartan matrix; global dimension.

    • Abstract

       

      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.

    • Author Affiliations

       

      Umesh V Dubey1 Amritanshu Prasad1 Pooja Singla2

      1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
      2. Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel

    • Dates

       
      Published
      February 2012
      Manuscript received
      20 December 2010

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