Research Article
Year 2018,
Volume: 18 Issue: 1, 131 - 155, 30.04.2018
Abstract
Bu makalede, O karakteristiği 2 ve 3 den farklı bir R cismi üzerinde tanımlı bir octonion (Cayley-
Dickson) R-cebiri, O ve 2 0 olmak üzere girdileri A O O lokal halkasından alınarak
oluşturulan 3x3 matris uzayının 3 , J H A 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.
References
- Akpınar, A., 2007. Geometrik Yapılarda Çifte Oran. Doktora Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 84.
- Beachy, J.A., 1999. Introductory Lectures on Rings and Modules. London Mathematical Society Student Texts 47, Cambridge Univ. Press, UK, 238.
- Benz, W., 1973. Vorlesungen über Geometrie der Algebren. Springer, Berlin, 368.
- Bix, R., 1980. Octonion planes over local rings. Trans. Amer. Math. Soc., 261(2), 417-438.
- Blunck, A., 1991. Cross-Ratios Over Lokal Alternative Rings. Result Math., 19, 246-256.
- Blunck, A., 1992. Cross-ratios in Moufang-Klingenberg planes. Geometriae Dedicata, 43, 93-107.
- Blyth, T.S. and Robertson E.F., 2002. Further Linear Algebra. Springer, UK, 230.
- Çelik, B., 1995. Non-Assosyatif Cebirler Üzerine Kurulan Projektif Yapılar. Doktora Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 77.
- Çiftçi, S., 2015. Lineer Cebir. Dora Basın Yayın Dağıtım, Bursa, 430.
- Elman, R., Karpenko, N. and Merkurjev, A., 2008. The Algebraic and Geometric Theory of Quadratic Forms. Amer. Math. Soc., Colloguium Publications, 56, 443.
- Faulkner, J.R., 1970. Octonion planes defined by quadratic Jordan algebras. Mem. Amer. Math. Soc., 104, 71.
- Faulkner, J.R., 2014. The Role of Nonassociative Algebra in Projective Geometry. Graduate Studies in Mathematics, 159, Amer. Math. Soc., Providence, R.I., 229.
- Fraleigh, J.B., 1982. A First Course in Abstract Algebra. Third Edition, Addison-Wesley Publishing Company, 478.
- Freudenthal, H., 1951. Octaven, Ausnahmegruppen, und Octavengeometrie. Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 49.
- Hungerford, T.W., 1974. Algebra. Holt Rinehart and Winston, Inc., New York, 502.
- Jacobson, N., 1968. Structure and Representations of Jordan Algebras. Colloq. Publ., 39, Amer. Math. Soc., Providence, R.I., 453.
- Jacobson N., 1969. Lectures on Quadratic Jordan Algebras. Lecture Notes. Tata Institute of Fundamental Research, Bombay, 128.
- Jacobson, N., 1985. Basic Algebra I. Second Edition, W.H. Freeman and Company, New York, 499.
- Jordan, P., 1949. Über Eine Nicht-Desarguessche Ebene Projektive Geometrie. Abh. Math. Sem. Univ. Hamburg, 16, 74-76.
- Malik, D.S., Mordeson, J.M. and Sen M.K., 1997. Fundementals of Abstract Algebra. The McGraw-Hill, New York, 636.
- McCrimmon K., 1969. The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras. Trans. Amer. Math. Soc., 139, 495-510.
- McCrimmon, K., 2004. A Taste of Jordan Algebras. Springer, New York, 562.
- McDonald, B.R., 1976. Geometric Algebra over Local Rings. Marcel Dekker, Inc., New York and Basel, 421.
- Moufang, R., 1933. Alternativekörper und der Satz vom vollstandigen Verseit. Abh. Math. Sem. Univ. Hamburg, 9, 207-222.
- Özkan, İ., 2016. Lokal Halkalar Üzerine Octonion Düzlemler. Yüksek Lisans Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 85.
- Pickert, G., 1955. Projektive Ebenen. Springer, Berlin, 343.
- Schafer, R.D., 1996. An Introduction to Nonassociative Algebras. Dover Publications Inc., New York, 166.
- Springer, T.A., 1960. The Projective Octave Plane. Nederl. Akad. Wetensch. Proc. Ser. A, 63, Indag. Math., 22, 74-101.
- Stevenson, F.W., 1972. Projective Planes. W. H. Freeman and Company, San Francisco, USA, 416.
- Thomas, E.G.F., 2014. A Polarization Identity for Multilinear Maps. Indagationes Mathematicae, 25, 468-474.
Year 2018,
Volume: 18 Issue: 1, 131 - 155, 30.04.2018
Abstract
References
- Akpınar, A., 2007. Geometrik Yapılarda Çifte Oran. Doktora Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 84.
- Beachy, J.A., 1999. Introductory Lectures on Rings and Modules. London Mathematical Society Student Texts 47, Cambridge Univ. Press, UK, 238.
- Benz, W., 1973. Vorlesungen über Geometrie der Algebren. Springer, Berlin, 368.
- Bix, R., 1980. Octonion planes over local rings. Trans. Amer. Math. Soc., 261(2), 417-438.
- Blunck, A., 1991. Cross-Ratios Over Lokal Alternative Rings. Result Math., 19, 246-256.
- Blunck, A., 1992. Cross-ratios in Moufang-Klingenberg planes. Geometriae Dedicata, 43, 93-107.
- Blyth, T.S. and Robertson E.F., 2002. Further Linear Algebra. Springer, UK, 230.
- Çelik, B., 1995. Non-Assosyatif Cebirler Üzerine Kurulan Projektif Yapılar. Doktora Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 77.
- Çiftçi, S., 2015. Lineer Cebir. Dora Basın Yayın Dağıtım, Bursa, 430.
- Elman, R., Karpenko, N. and Merkurjev, A., 2008. The Algebraic and Geometric Theory of Quadratic Forms. Amer. Math. Soc., Colloguium Publications, 56, 443.
- Faulkner, J.R., 1970. Octonion planes defined by quadratic Jordan algebras. Mem. Amer. Math. Soc., 104, 71.
- Faulkner, J.R., 2014. The Role of Nonassociative Algebra in Projective Geometry. Graduate Studies in Mathematics, 159, Amer. Math. Soc., Providence, R.I., 229.
- Fraleigh, J.B., 1982. A First Course in Abstract Algebra. Third Edition, Addison-Wesley Publishing Company, 478.
- Freudenthal, H., 1951. Octaven, Ausnahmegruppen, und Octavengeometrie. Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 49.
- Hungerford, T.W., 1974. Algebra. Holt Rinehart and Winston, Inc., New York, 502.
- Jacobson, N., 1968. Structure and Representations of Jordan Algebras. Colloq. Publ., 39, Amer. Math. Soc., Providence, R.I., 453.
- Jacobson N., 1969. Lectures on Quadratic Jordan Algebras. Lecture Notes. Tata Institute of Fundamental Research, Bombay, 128.
- Jacobson, N., 1985. Basic Algebra I. Second Edition, W.H. Freeman and Company, New York, 499.
- Jordan, P., 1949. Über Eine Nicht-Desarguessche Ebene Projektive Geometrie. Abh. Math. Sem. Univ. Hamburg, 16, 74-76.
- Malik, D.S., Mordeson, J.M. and Sen M.K., 1997. Fundementals of Abstract Algebra. The McGraw-Hill, New York, 636.
- McCrimmon K., 1969. The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras. Trans. Amer. Math. Soc., 139, 495-510.
- McCrimmon, K., 2004. A Taste of Jordan Algebras. Springer, New York, 562.
- McDonald, B.R., 1976. Geometric Algebra over Local Rings. Marcel Dekker, Inc., New York and Basel, 421.
- Moufang, R., 1933. Alternativekörper und der Satz vom vollstandigen Verseit. Abh. Math. Sem. Univ. Hamburg, 9, 207-222.
- Özkan, İ., 2016. Lokal Halkalar Üzerine Octonion Düzlemler. Yüksek Lisans Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü, Bursa, 85.
- Pickert, G., 1955. Projektive Ebenen. Springer, Berlin, 343.
- Schafer, R.D., 1996. An Introduction to Nonassociative Algebras. Dover Publications Inc., New York, 166.
- Springer, T.A., 1960. The Projective Octave Plane. Nederl. Akad. Wetensch. Proc. Ser. A, 63, Indag. Math., 22, 74-101.
- Stevenson, F.W., 1972. Projective Planes. W. H. Freeman and Company, San Francisco, USA, 416.
- Thomas, E.G.F., 2014. A Polarization Identity for Multilinear Maps. Indagationes Mathematicae, 25, 468-474.
There are 30 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | April 30, 2018 |
| Submission Date | August 15, 2016 |
| Published in Issue | Year 2018 Volume: 18 Issue: 1 |