$Amathcal{T}$-Algebras and Extensions of $AT$-Algebras

Proceedings Mathematical Sciences

Hongliang Yao¹ 

[1] School of Science, Nanjing University of Science and Technology, Nanjing 00, People’s Republic of China$$

关键词: 𝐴𝐹-algebra;    $Amathbb{T}$-algebra;    $Amathcal{T}$-algebra;    extension;    index map.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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

【 授权许可】

Unknown