The upper triangular algebra loop of degree 4
Munywoki, Michael, M.
Smith, Jonathan D.H
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A natural loop structure is defined on the set U4 of unimodular uppertriangular 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 detailed 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.