Date of Award
Master of Science
Jonathan D. Smtih
A natural loop structure is defined on the set U_4 of the set of 4x4 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 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.
Michael Mbindyo Munywoki
Munywoki, Michael Mbindyo, "The upper triangular algebra loop of degree 4" (2015). Graduate Theses and Dissertations. 14607.