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.
|Original language||English (US)|
|Number of pages||14|
|Journal||Commentationes Mathematicae Universitatis Carolinae|
|State||Published - Jan 1 2014|
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