On certain finite-dimensional algebras generated by two idempotents

✍ Scribed by A. Böttcher; I.M. Spitkovsky

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 272 KB
• Volume: 435
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2011.03.046

✦ Synopsis

This paper is concerned with algebras generated by two idempotents P and Q satisfying (PQ ) m = (QP) m and (PQ ) m-1 = (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.