双对角三元组与四面体代数
Bidiagonal Triads and the Tetrahedron Algebra
摘要：
我们引入一个线性代数对象称为双对角三元组。双对角三元组是以前研究过的双对角三元组概念的修改。双对角三元组和双对角三元组都由有限维向量空间上的三个可对角化的线性变换组成，每个变换都以双对角方式作用于另外两个变换的特征空间。三元组与三元组的不同之处在于这些双对角线作用的定义方式。本文将有关双对角三元组的一些定理修正到双对角三元组的情形。我们还描述了双对角三元组与四面体李代数的表示论之间的密切关系。
英文摘要：
We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad is a modification of the previously studied and similarly defined concept of bidiagonal triple. A bidiagonal triad and a bidiagonal triple both consist of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other two. A triad differs from a triple in the way these bidiagonal actions are defined. We modify a number of theorems about bidiagonal triples to the case of bidiagonal triads. We also describe the close relationship between bidiagonal triads and the representation theory of the tetrahedron Lie algebra.
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