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Journals / Cumhuriyet Science Journal / 2018 / Cilt: 39 - Sayı: 2

Some Results On Quaternion 3-Space

Kuaterniyon 3-Uzay Üzerine Bazı Sonuçlar

Atilla AKPINAR
Fatma OZEN ERDOGAN
Pages
303–313
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

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

Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q, the obtained results are carried toa more general state.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, with entries in a quaternion F-algebra Q, thatare symmetric with respect to the canonical involution Jγ is studied.
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Key Findings & Data:J′ is also the special Jordan matrixalgebra and some results related to points and lines of the quaternion 3-space P(J′) defined by the algebra areintroduced.
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Conclusion & Impact:Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q, the obtained results are carried toa more general state.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, with entries in a quaternion F-algebra Q, thatare symmetric with respect to the canonical involution Jγ is studied. J′ is also the special Jordan matrixalgebra and some results related to points and lines of the quaternion 3-space P(J′) defined by the algebra areintroduced. Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q, the obtained results are carried toa more general state.

Özet

Bu makalede, girdileri bir Q kuaterniyon F-cebirinden alınan ve Jγ kanonik involusyonuna göre simetrik olan 4×4 boyutlu matrislerin oluşturduğu J′=H(Q₄,Jγ) kümesi ile çalışılmıştır. Bu J′ kümesi aynı zamanda bir özel Jordan matris cebiridir ve bu cebir ile tanımlanan P(J′) kuaterniyon 3-uzayın noktalar ve doğruları ile ilgili bazı sonuçlar sunulmuştur. Son olarak, Q yerine Q:= Q+Qε (ε∉Q, ε²=0) dual halkası alınarak elde edilen sonuçlar daha genel bir duruma taşınmıştır

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Cite This Article

AKPINAR, A., ERDOGAN, F. O. (2022). Some Results On Quaternion 3-Space. Cumhuriyet Science Journal, Cilt: 39 - Sayı: 2, 303–313. https://ajindex.com/articles/477970

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References (8)

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