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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2018 / Cilt: 18 - Sayı: 1

Quadratic (Exceptional) Jordan Algebra of Dimension 54

54 Boyutlu (Exceptional) Kuadratik Jordan Cebiri

Atilla AKPINAR
Pages
131–155
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A cubic algebra structure is first constructed by a norm form (determinant of a matrix) and a trace form (trace of a matrix) on the set, and so it is obtained (exceptional) quadratic Jordan algebra of dimension 54.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, the special subset of symmetric elements denoted by   3,JAH of 3x3 matrix spaces, whose entries are taken from  A OO local ring where O is an octonion (Cayley-Dickson) algebra defined over a field of characteristic not two and three, O and 2 0   , is studied.
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Key Findings & Data:In this paper, the special subset of symmetric elements denoted by   3,JAH of 3x3 matrix spaces, whose entries are taken from  A OO local ring where O is an octonion (Cayley-Dickson) algebra defined over a field of characteristic not two and three, O and 2 0   , is studied.
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Conclusion & Impact:A cubic algebra structure is first constructed by a norm form (determinant of a matrix) and a trace form (trace of a matrix) on the set, and so it is obtained (exceptional) quadratic Jordan algebra of dimension 54.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, the special subset of symmetric elements denoted by   3,JAH of 3x3 matrix spaces, whose entries are taken from  A OO local ring where O is an octonion (Cayley-Dickson) algebra defined over a field of characteristic not two and three, O and 2 0   , is studied. A cubic algebra structure is first constructed by a norm form (determinant of a matrix) and a trace form (trace of a matrix) on the set, and so it is obtained (exceptional) quadratic Jordan algebra of dimension 54.

Özet

Bu makalede, O karakteristiği 2 ve 3 den farklı bir R cismi üzerinde tanımlı bir octonion (CayleyDickson) R-cebiri,  O ve 2 0   olmak üzere girdileri  A OO lokal halkasından alınarak oluşturulan 3x3 matris uzayının   3,JAH ile gösterilen simetrik elemanlarının bir özel alt kümesi ile çalışılmıştır. Bu küme üzerinde bir norm form (determinant) ve bir iz form (bir matrisin izi) yardımıyla önce bir kübik cebir yapısı kurulmuş ve bu sayede 54 boyutlu (exceptional) kuadratik Jordan cebiri elde edilmiştir.

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Cite This Article

AKPINAR, A. (2022). Quadratic (Exceptional) Jordan Algebra of Dimension 54. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 18 - Sayı: 1, 131–155. https://ajindex.com/articles/430027

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