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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/110/03/0263-0292

    • Keywords

       

      Equivalence relations; Bratteli diagrams; G-relations

    • Abstract

       

      In this paper, we study a tower {AnG: n} ≥ 1 of finite-dimensional algebras; here, G represents an arbitrary finite group,d denotes a complex parameter, and the algebraAnG(d) has a basis indexed by ‘G-stable equivalence relations’ on a set whereG acts freely and has 2n orbits. We show that the algebraAnG(d) is semi-simple for all but a finite set of values ofd, and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the ‘generic case’. Finally we determine the Bratteli diagram of the tower {AnG(d): n} ≥ 1 (in the generic case).

    • Author Affiliations

       

      Vijay Kodiyalam1 R Srinivasan1 V S Sunder1

      1. Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai - 600 113, India

    • Dates

       
      Published
      August 2000
      Manuscript received
      30 November 1999

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