Title

On certain finite-dimensional algebras generated by two idempotents

Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2011

Volume

435

Issue

8

First Page

1823

Abstract

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.

DOI

10.1016/j.laa.2011.03.046

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