On certain finite-dimensional algebras generated by two idempotents

A. Böttcher; I. M. Spitkovsky

doi:10.1016/j.laa.2011.03.046

On certain finite-dimensional algebras generated by two idempotents

A. Böttcher, I. M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1823-1836
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	435
Issue number	8
DOIs	https://doi.org/10.1016/j.laa.2011.03.046
State	Published - Oct 15 2011

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

Access to Document

10.1016/j.laa.2011.03.046

Cite this

@article{aaa7ab1cb002438e800fb2d12c9bec72,

title = "On certain finite-dimensional algebras generated by two idempotents",

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.",

keywords = "Drazin inversion, Finite-dimensional algebra, Group inversion, Idempotent, Skew and oblique projection",

author = "A. B{\"o}ttcher and Spitkovsky, {I. M.}",

year = "2011",

month = oct,

day = "15",

doi = "10.1016/j.laa.2011.03.046",

language = "English (US)",

volume = "435",

pages = "1823--1836",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "8",

}

TY - JOUR

T1 - On certain finite-dimensional algebras generated by two idempotents

AU - Böttcher, A.

AU - Spitkovsky, I. M.

PY - 2011/10/15

Y1 - 2011/10/15

N2 - 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.

AB - 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.

KW - Drazin inversion

KW - Finite-dimensional algebra

KW - Group inversion

KW - Idempotent

KW - Skew and oblique projection

UR - http://www.scopus.com/inward/record.url?scp=79958796229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958796229&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2011.03.046

DO - 10.1016/j.laa.2011.03.046

M3 - Article

AN - SCOPUS:79958796229

SN - 0024-3795

VL - 435

SP - 1823

EP - 1836

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 8

ER -

On certain finite-dimensional algebras generated by two idempotents

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this