The upper triangular algebra loop of degree 4

Kenneth Johnson, M. Munywoki, Jonathan D.H. Smith

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)457-470
Number of pages14
JournalCommentationes Mathematicae Universitatis Carolinae
Volume55
Issue number4
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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