On certain finite-dimensional algebras generated by two idempotents

A. Böttcher, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1823-1836
Number of pages14
JournalLinear Algebra and Its Applications
Volume435
Issue number8
DOIs
StatePublished - Oct 15 2011

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Finite Dimensional Algebra
Idempotent
Algebra
Group Inverse
Invertible
Term

Keywords

  • Drazin inversion
  • Finite-dimensional algebra
  • Group inversion
  • Idempotent
  • Skew and oblique projection

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

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

In: Linear Algebra and Its Applications, Vol. 435, No. 8, 15.10.2011, p. 1823-1836.

Research output: Contribution to journalArticle

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