Araştırma Makalesi
Yıl 2018,
Cilt: 39 Sayı: 2, 303 - 313, 29.06.2018
Öz
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.
Anahtar Kelimeler
Kaynakça
- [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.
Yıl 2018,
Cilt: 39 Sayı: 2, 303 - 313, 29.06.2018
Öz
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.
Anahtar Kelimeler
Kaynakça
- [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.
Toplam 9 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Natural Sciences |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Haziran 2018 |
| Gönderilme Tarihi | 10 Nisan 2017 |
| Kabul Tarihi | 10 Nisan 2018 |
| Yayımlandığı Sayı | Yıl 2018Cilt: 39 Sayı: 2 |