On certain finite-dimensional algebras generated by two idempotents

被引：12

作者：

Boettcher, A. ^{[2
]}

Spitkovsky, I. M. ^{[1
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[2] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 08期

关键词：

Finite-dimensional algebra; Idempotent; Skew and oblique projection; Drazin inversion; Group inversion; ORTHOGONAL PROJECTIONS; INVERTIBILITY SYMBOLS; EXTENSION-THEOREMS; BANACH-ALGEBRAS; DRAZIN-INVERSES;

D O I：

10.1016/j.laa.2011.03.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with algebras generated by two idempotents P and Q satisfying (PQ)(m) = (QP)(m) and (PQ)(m-1) not equal (QP)(m-1). The main result is the classification of all these algebras, implying that for each m >= 2 there exist exactly eight nonisomorphic copies. As an application, it is shown that if an element of such an algebra has a nondegenerate leading term, then it is group invertible, and a formula for the explicit computation of the group inverse is given. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1823 / 1836

页数：14

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