• $A\mathcal{T}$-Algebras and Extensions of $AT$-Algebras

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      https://www.ias.ac.in/article/fulltext/pmsc/120/02/0199-0207

    • Keywords

       

      $AF$-algebra; $A\mathbb{T}$-algebra; $A\mathcal{T}$-algebra; extension; index map.

    • Abstract

       

      Lin and Su classified $A\mathcal{T}$-algebras of real rank zero. This class includes all $A\mathbb{T}$-algebras of real rank zero as well as many $C^∗$-algebras which are not stably finite. An $A\mathcal{T}$-algebra often becomes an extension of an $A\mathbb{T}$-algebra by an $AF$-algebra. In this paper, we show that there is an essential extension of an $A\mathbb{T}$-algebra by an $AF$-algebra which is not an $A\mathcal{T}$-algebra. We describe a characterization of an extension 𝐸 of an $A\mathbb{T}$-algebra by an $AF$-algebra if 𝐸 is an $A\mathcal{T}$-algebra.

    • Author Affiliations

       

      Hongliang Yao1 2

      1. School of Science, Nanjing University of Science and Technology, Nanjing 210014, People’s Republic of China
      2. Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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