Full algebras of matrices

被引：4

作者：

Cigler, Grega ^{[1
]}

Jerman, Marjan ^{[1
]}

Wojciechowski, Piotr J. ^{[2
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[2] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 08期

关键词：

Algebra of matrices; transitive graph; lattice order;

D O I：

10.1080/03081087.2018.1460792

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A classification of full algebras of matrices is given. All such algebras are permutation-isomorphic to block lower-triangular matrices with corresponding subdiagonal blocks being either zero-blocks or full. Two full algebras are isomorphic if and only if they are permutation-isomorphic. A one-to-one correspondence is provided between the full algebras and transitive directed graphs. It is also proven that such algebras, if endowed with a lattice order, can be almost f- or d-algebras only if they are diagonal.

引用

页码：1511 / 1521

页数：11