Group inversion in certain finite-dimensional algebras generated by two idempotents

A. Böttcher, Ilya Spitkovsky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)715-732
Number of pages18
JournalIndagationes Mathematicae
Volume23
Issue number4
DOIs
StatePublished - Dec 1 2012

Fingerprint

Finite Dimensional Algebra
Idempotent
Invertibility
Inversion
Algebra
Banach algebra
Theorem

Keywords

  • Finite-dimensional algebra
  • Group inversion
  • Idempotent
  • Two projections

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Group inversion in certain finite-dimensional algebras generated by two idempotents. / Böttcher, A.; Spitkovsky, Ilya.

In: Indagationes Mathematicae, Vol. 23, No. 4, 01.12.2012, p. 715-732.

Research output: Contribution to journalArticle

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