An algebra governing reduction of quaternary structures to ternary structures III. A study of generators of the resulting algebra
Journal Title: Bulletin de la Société des sciences et des lettres de Łódź, Série: Recherches sur les déformations - Year 2016, Vol 0, Issue 1
Abstract
By applying the reduction matrices of Part I we analyzed in Part II the multiplication tables of generators of the cubic and nonion algebras, deduced the remaining 3 x 3 sub- tables for the resulting algebra, determined the remaining 9 generators, and studied the corresponding multiplication tables. In this, Part III of the paper, we consider the problem of linear independence of the resulting generators. After checking the dimension 18 of the algebra (duodevicenion algebra), we extend the Peirce-Sylvester matrix quarter-plane to the whole plane. Choose in each quarter the generator related bridging scales, and analyse from that point of view the resulting duodevicenion algebra and other related \daughter al- gebras": quasi-quaternion, quasi-para-quaternion, quasi-octonion and quasi-para-octonion.
Authors and Affiliations
Małgorzata Nowak-Kępczyk
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