Bu çalışmada, S3permütasyon grupları üzerine kurulmuş kesirsel süpersimetrik iso 1,1 cebri, Hopf cebri formülasyonunda elde edilmiştir. Bu cebir U 2 3 iso 1.1 ile gösterilmiştir.
Ahmedov H and Dayi Ö. F. (1999)..,Two dimensional fractional supersymmetry from
the quantum Poincare group at roots of unity, J.Phys.A, V.32, 6247-625.
Ahmedov H and Dayi Ö. F. (2000).,Non-abeian fractional supersymmetry in two
dimensions,Mod.Phys.Lett.A, V.15, No.29 ,1801-18111.
Ahmedov, H. and Dayi, Ö. F. (1999). 𝑆𝐿𝑞(2, ℝ) at roots of unity. J. Phys. A: Math.
Gen. 32 1895-1907.
Ahmedov, H., Yildiz, A. and Ucan, Y. (2001). Fractional Super Lie Algebras and
Groups, J. Phys. A: Math. Gen. 34 6413-6423.
Ahn C, Bernard D. and Leclair A. (1990). Fractional supersymmetries in perturbed
coset CFT.s and intrgrable soliton theory, Nucl.Phys.B, 409.
De Witt B. (1992) Supermanifolds(Cambridge Monographs on Mathematical
Physics), 428. Cambridge University Press; 2th Edition, Cambridge.
Goze M., Raush deTraunbenberg M. and Tanasa A. J. (2007), Poincaré and sl(2)
algebras of order 3, Math. Phys., 48, 093507.
Kerner R. (1992), 𝑍3
-graded algebras and the cubic root of the supersymmetry
translations, J. Math. Phys. 33,403.
Kostant B. (1997). Graded manifolds, graded Lie theory and prequantization Lecture
Notes in Mathematics,177. Springer, Berlin.
Raush de Traunbenberg M. (2004) Four Dimensional Cubic Supersymmetry,
Proceedings of institute of Mathematics of NAS of Ukraine, 50 part 2, 578-585.
Rausch de Traubenberg M. and Slupinski M. J.(1997) Fractional supersymmetry and
groups,Mod. Phys. Lett.A, 39, 3051.
Rausch de Traubenberg M. and Slupinski M. J.(2000), Fractional supersymmetry and
Fth-roots of representations,J. Math. Phys., 41, 4556.
Vilenkin N. Ya. and Klimyk A. U. (1991). Representations of Lie Groups and Special
Functions, Kluwer, Academic, Dordrecht.
Wang X., Han D., Yu C. And Zheng Z. (2012). The geometric structure of unit dual
quaternion with application in kinematic control. J. Math. Anal. Appl. 389 1352–
1364.
In this study, fractional supersymmetric iso 1,1 based on the permutation groups S3, formulated in the Hopf algebra is obtained. This algebra is denoted by U 32 iso 1,1 .
Ahmedov H and Dayi Ö. F. (1999)..,Two dimensional fractional supersymmetry from
the quantum Poincare group at roots of unity, J.Phys.A, V.32, 6247-625.
Ahmedov H and Dayi Ö. F. (2000).,Non-abeian fractional supersymmetry in two
dimensions,Mod.Phys.Lett.A, V.15, No.29 ,1801-18111.
Ahmedov, H. and Dayi, Ö. F. (1999). 𝑆𝐿𝑞(2, ℝ) at roots of unity. J. Phys. A: Math.
Gen. 32 1895-1907.
Ahmedov, H., Yildiz, A. and Ucan, Y. (2001). Fractional Super Lie Algebras and
Groups, J. Phys. A: Math. Gen. 34 6413-6423.
Ahn C, Bernard D. and Leclair A. (1990). Fractional supersymmetries in perturbed
coset CFT.s and intrgrable soliton theory, Nucl.Phys.B, 409.
De Witt B. (1992) Supermanifolds(Cambridge Monographs on Mathematical
Physics), 428. Cambridge University Press; 2th Edition, Cambridge.
Goze M., Raush deTraunbenberg M. and Tanasa A. J. (2007), Poincaré and sl(2)
algebras of order 3, Math. Phys., 48, 093507.
Kerner R. (1992), 𝑍3
-graded algebras and the cubic root of the supersymmetry
translations, J. Math. Phys. 33,403.
Kostant B. (1997). Graded manifolds, graded Lie theory and prequantization Lecture
Notes in Mathematics,177. Springer, Berlin.
Raush de Traunbenberg M. (2004) Four Dimensional Cubic Supersymmetry,
Proceedings of institute of Mathematics of NAS of Ukraine, 50 part 2, 578-585.
Rausch de Traubenberg M. and Slupinski M. J.(1997) Fractional supersymmetry and
groups,Mod. Phys. Lett.A, 39, 3051.
Rausch de Traubenberg M. and Slupinski M. J.(2000), Fractional supersymmetry and
Fth-roots of representations,J. Math. Phys., 41, 4556.
Vilenkin N. Ya. and Klimyk A. U. (1991). Representations of Lie Groups and Special
Functions, Kluwer, Academic, Dordrecht.
Wang X., Han D., Yu C. And Zheng Z. (2012). The geometric structure of unit dual
quaternion with application in kinematic control. J. Math. Anal. Appl. 389 1352–
1364.
Reşat Köşker
Bu kişi benim
Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering, Department of Mathematical Engineering, İstanbul, Turkey
Özge Hıdırlar
Bu kişi benim
Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering, Department of Mathematical Engineering, İstanbul, Turkey