### 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) |
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Pages (from-to) | 457-470 |

Number of pages | 14 |

Journal | Commentationes Mathematicae Universitatis Carolinae |

Volume | 55 |

Issue number | 4 |

State | Published - Jan 1 2014 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Johnson, K., Munywoki, M., & Smith, J. D. H. (2014). The upper triangular algebra loop of degree 4.

*Commentationes Mathematicae Universitatis Carolinae*,*55*(4), 457-470.