Research Article
Year 2018,
Volume: 39 Issue: 2, 303 - 313, 29.06.2018
Abstract
In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, with
entries in a quaternion F-algebra Q, that are symmetric with respect to the
canonical involution Jγ is studied. J′
is also the special Jordan matrix algebra and some results related to points
and lines of the quaternion 3-space P(J′)
defined by the algebra are introduced. Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q,
the obtained results are carried to a more general state.
entries in a quaternion F-algebra Q, that are symmetric with respect to the
canonical involution Jγ is studied. J′
is also the special Jordan matrix algebra and some results related to points
and lines of the quaternion 3-space P(J′)
defined by the algebra are introduced. Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q,
the obtained results are carried to a more general state.
References
- [1]. Akpinar, A. and Erdogan, F.O., Dual Quaternionic (n-1)-Spaces Defined by Special Jordan Algebras of Dimension 4n²-2n, 2018 (under review)
- [2]. Akpinar, A. and Erdogan, F.O., Collineations and Cross-Ratios in Octonion Planes, 2018 (under review)
- [3]. Celik, B. and Erdogan, F.O., On Addition and Multiplication of Points in a Certain Class of Projective Klingenberg Planes, Journal of Inequalities and Applications, 230 (2013).
- [4]. Celik, B. and Dayioglu, A., The Collineations which Act as Addition and Multiplication on Points in a Certain Class of Projective Klingenberg Planes, Journal of Inequalities and Applications, 193 (2013).
- [5]. Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970) 1-71.
- [6]. Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., (2014).
- [7]. Jacobson, N., Structure and Representations of Jordan Algebras, Colloq. Publ. 39, Amer. Math. Soc., Providence, R.I., (1968).
- [8]. Jacobson, N., Basic Algebra I, W. H. Freeman and Company, New York, (1985).
- [9]. McCrimmon, K., The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras, Trans. of the Amer. Math. Soc., 139 (1969) 495-510.
Year 2018,
Volume: 39 Issue: 2, 303 - 313, 29.06.2018
Abstract
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.
References
- [1]. Akpinar, A. and Erdogan, F.O., Dual Quaternionic (n-1)-Spaces Defined by Special Jordan Algebras of Dimension 4n²-2n, 2018 (under review)
- [2]. Akpinar, A. and Erdogan, F.O., Collineations and Cross-Ratios in Octonion Planes, 2018 (under review)
- [3]. Celik, B. and Erdogan, F.O., On Addition and Multiplication of Points in a Certain Class of Projective Klingenberg Planes, Journal of Inequalities and Applications, 230 (2013).
- [4]. Celik, B. and Dayioglu, A., The Collineations which Act as Addition and Multiplication on Points in a Certain Class of Projective Klingenberg Planes, Journal of Inequalities and Applications, 193 (2013).
- [5]. Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970) 1-71.
- [6]. Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., (2014).
- [7]. Jacobson, N., Structure and Representations of Jordan Algebras, Colloq. Publ. 39, Amer. Math. Soc., Providence, R.I., (1968).
- [8]. Jacobson, N., Basic Algebra I, W. H. Freeman and Company, New York, (1985).
- [9]. McCrimmon, K., The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras, Trans. of the Amer. Math. Soc., 139 (1969) 495-510.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | April 10, 2017 |
| Acceptance Date | April 10, 2018 |
| Publication Date | June 29, 2018 |
| DOI | https://doi.org/10.17776/csj.434228 |
| IZ | https://izlik.org/JA68RD64UG |
| Published in Issue | Year 2018 Volume: 39 Issue: 2 |
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