The upper triangular algebra loop of degree 4
Date
2015-01-01
Authors
Munywoki, Michael
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Jonathan D. Smtih
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Mathematics
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Abstract
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.
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Thu Jan 01 00:00:00 UTC 2015