Dejenere Clifford Cebirleri ve Temsilleri

Öz

Bu çalışmada dejenere Clifford cebirlerinden dejenere olmayan Clifford cebirlerine bir gömme teoremi verdik. Dejenere olmayan Clifford Cebirlerinin temsillerini kullanarak dejenere Clifford cebirlerinin temsilleri için bir metod geliştirdik. Düşük boyutlar için bazı açık temsilleri verdik

Anahtar Kelimeler

• Dejenere Clifford cebri, Clifford cebirlerinin temsili, kuadratik form, nilpotent ideal

Degenerate Clifford Algebras and Their Reperesentations

Öz

In this study, we give an imbedding theorem for a degenerate Clifford algebra into nondegenerate one. By using the representations of non-degenerate Clifford algebra we develop a method for the representations of the degenerate Clifford algebras. We give some explicit constructions for lower dimensions

Anahtar Kelimeler

• Degenerate Clifford algebra, representation of Clifford algebras, quadratic form, nilpotent ideal

Kaynakça

1. T. Friedrich, Dirac Operators in Riemannian Geometry, AMS, (2000).
2. R. Harvey, Spinors and Calibrations, Academic Press, (1990).
3. H.B. Lawson and M.L. Michelsohn, Spin Geometry, Princeton Univ., (1989).
4. R. Ablamowicz, Structure of spin groups associated with degenerate Clifford algebras, Journal of Mathematical Physics 27, (1986).
5. N. Değirmenci and Ş. Karapazar, Explicit Isomorphisms of Real Clifford Algebras, International Journal of Mathematics and Mathematical Sciences, (2006).
6. M. F. Atiyah, R. Bott and V.K. Shapiro, Clifford Modules, Topology, 3, 1, 3-38, (1964).
7. A.Dimaskis, A new representation of Clifford Algebras, Journal of Physics A: Mathematical and Theoretical., 22, 3171-3193 (1989).
8. A.Trautman, Clifford Algebras and Their Representations, Encyclopedia of Mathematical Physics, (2005).

9. N. Değirmenci and Ş. Koçak, Generalized Self-Duality of 2-Forms, Advance in Applied Clifford Algebras, 13,107-113, (2003).
10. N. Değirmenci and N. Özdemir, The Construction of Maximum Independent Set of Matrices via Clifford Algebras, Turkish Journal of Mathematics, 31, 193-205, (2007).
11. H. Baum and I. Kath, Parallel spinors and holonomy groups on pseudo- Riemannian spin manifolds, Annals of Global Analysis and Geometry, 17, 1-17, (1999).
12. C. Faith, Algebra I: Rings, Modules, and Categories, Springer-Verlag, (1973).
13. D. R. Farenick, Algebras of Linear Transformations, Springer-Verlag, (2001)