"Group inversion in certain finite-dimensional algebras generated by tw" by A. Boettcher and I. M. Spitkovsky
 

Document Type

Article

Department/Program

Mathematics

Journal Title

Indagationes Mathematicae-New Series

Pub Date

2012

Volume

23

Issue

4

First Page

715

Abstract

Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents. (c) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

DOI

10.1016/j.indag.2012.08.006

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