### Abstract

A natural loop structure is defined on the set U_{4} of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A de- tailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.

Original language | English (US) |
---|---|

Pages (from-to) | 457-470 |

Number of pages | 14 |

Journal | Commentationes Mathematicae Universitatis Carolinae |

Volume | 55 |

Issue number | 4 |

State | Published - Jan 1 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Commentationes Mathematicae Universitatis Carolinae*,

*55*(4), 457-470.

}

*Commentationes Mathematicae Universitatis Carolinae*, vol. 55, no. 4, pp. 457-470.

**The upper triangular algebra loop of degree 4.** / Johnson, Kenneth; Munywoki, M.; Smith, Jonathan D.H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The upper triangular algebra loop of degree 4

AU - Johnson, Kenneth

AU - Munywoki, M.

AU - Smith, Jonathan D.H.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A natural loop structure is defined on the set U4 of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A de- tailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.

AB - A natural loop structure is defined on the set U4 of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A de- tailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.

UR - http://www.scopus.com/inward/record.url?scp=84907759442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907759442&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84907759442

VL - 55

SP - 457

EP - 470

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

SN - 0010-2628

IS - 4

ER -