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A Two-parameter Deformation of Supergroup GL(1|2)

Yıl 2018, Cilt: 8 Sayı: 4, 271 - 279, 30.12.2018

Sultan Abacı Çelik

https://doi.org/10.21597/jist.412142
Cited By: 1

Öz

A new super-Hopf algebra, denoted by , is obtained by using the standard method (the RTT-relation)

with an R-matrix which is a solution of the quantum Yang-Baxter equation.

Anahtar Kelimeler

Yang-Baxter equation super-Hopf algebra quantum supergroup

Kaynakça

  • Drinfeld V G, 1986. Quantum groups, Proc. I.C.M. Berkeley, 798-820.
  • Klimyk A and Schmüdgen K, Quantum Groups and Their Representations, Texts and Monographs in Physics, Springer, New York et al., 1997.
  • Majid, S., Foundtions of Quantum Group Theory, Cambridge Univ. press, 1995.
  • Yang C N, 1967. Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction, Phys. Rev. Lett. 19:1312-1314
  • Faddeev L D, Reshetikhin N Y and Takhtajan L A, 1990. Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1:193-225
  • Kobayashi T and Uematsu T, 1992. Differential calculus on the quantum superspace and deformation of phase space, Z.Phys. C 56:193-199
  • Berezin F A, 1987. Introduction to Algebra and Analysis with Anticommuting Variables, Reidel, Dordrecht.
  • Kulish P P and E.K.Sklyanin E K, 1982. Solutions of the Yang-Baxter equation, J.Soviet Mathematics 19:1596-1620
  • Celik S, 2016. Bicovariant differential calculus on the quantum superspace , J. Alg. App. 15:1650172-1-17.
  • Dabrowski L, and Wang, L, 1991. Two-parameter quantum deformation of GL(1|1), Phys. Lett. B. 266:51-54
  • Majid S, 1991. Examples of braided groups and braided matrices, J. Math. Phys. 32:3246-325
  • Schirrmacher A, 1991. The multiparametric deformation of GL(n) and the covariant differentil calculus on the quantum vector space, Z. Phys. C 50:321-327.

GL(1|2) Süper Grubunun Bir İki-parametreli Deformasyonu

Yıl 2018, Cilt: 8 Sayı: 4, 271 - 279, 30.12.2018

Sultan Abacı Çelik

https://doi.org/10.21597/jist.412142
Cited By: 1

Öz

Kuantum Yang-Baxter denkleminin çözümü olan bir R-matrisi yardımıyla, standard RTT-bağıntısı

kullanılarak ile gösterilen yeni bir süper-Hopf cebiri elde edilmiştir.

Anahtar Kelimeler

Yang-baxter equation super-hopf cebiri kuantum super grup

Kaynakça

  • Drinfeld V G, 1986. Quantum groups, Proc. I.C.M. Berkeley, 798-820.
  • Klimyk A and Schmüdgen K, Quantum Groups and Their Representations, Texts and Monographs in Physics, Springer, New York et al., 1997.
  • Majid, S., Foundtions of Quantum Group Theory, Cambridge Univ. press, 1995.
  • Yang C N, 1967. Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction, Phys. Rev. Lett. 19:1312-1314
  • Faddeev L D, Reshetikhin N Y and Takhtajan L A, 1990. Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1:193-225
  • Kobayashi T and Uematsu T, 1992. Differential calculus on the quantum superspace and deformation of phase space, Z.Phys. C 56:193-199
  • Berezin F A, 1987. Introduction to Algebra and Analysis with Anticommuting Variables, Reidel, Dordrecht.
  • Kulish P P and E.K.Sklyanin E K, 1982. Solutions of the Yang-Baxter equation, J.Soviet Mathematics 19:1596-1620
  • Celik S, 2016. Bicovariant differential calculus on the quantum superspace , J. Alg. App. 15:1650172-1-17.
  • Dabrowski L, and Wang, L, 1991. Two-parameter quantum deformation of GL(1|1), Phys. Lett. B. 266:51-54
  • Majid S, 1991. Examples of braided groups and braided matrices, J. Math. Phys. 32:3246-325
  • Schirrmacher A, 1991. The multiparametric deformation of GL(n) and the covariant differentil calculus on the quantum vector space, Z. Phys. C 50:321-327.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Sultan Abacı Çelik 0000-0003-3465-8209

Yayımlanma Tarihi 30 Aralık 2018
Gönderilme Tarihi 3 Nisan 2018
Kabul Tarihi 16 Temmuz 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 4

Kaynak Göster

APA Çelik, S. A. (2018). A Two-parameter Deformation of Supergroup GL(1|2). Journal of the Institute of Science and Technology, 8(4), 271-279. https://doi.org/10.21597/jist.412142
AMA Çelik SA. A Two-parameter Deformation of Supergroup GL(1|2). Iğdır Üniv. Fen Bil Enst. Der. Aralık 2018;8(4):271-279. doi:10.21597/jist.412142
Chicago Çelik, Sultan Abacı. “A Two-Parameter Deformation of Supergroup GL(1|2)”. Journal of the Institute of Science and Technology 8, sy. 4 (Aralık 2018): 271-79. https://doi.org/10.21597/jist.412142.
EndNote Çelik SA (01 Aralık 2018) A Two-parameter Deformation of Supergroup GL(1|2). Journal of the Institute of Science and Technology 8 4 271–279.
IEEE S. A. Çelik, “A Two-parameter Deformation of Supergroup GL(1|2)”, Iğdır Üniv. Fen Bil Enst. Der., c. 8, sy. 4, ss. 271–279, 2018, doi: 10.21597/jist.412142.
ISNAD Çelik, Sultan Abacı. “A Two-Parameter Deformation of Supergroup GL(1|2)”. Journal of the Institute of Science and Technology 8/4 (Aralık 2018), 271-279. https://doi.org/10.21597/jist.412142.
JAMA Çelik SA. A Two-parameter Deformation of Supergroup GL(1|2). Iğdır Üniv. Fen Bil Enst. Der. 2018;8:271–279.
MLA Çelik, Sultan Abacı. “A Two-Parameter Deformation of Supergroup GL(1|2)”. Journal of the Institute of Science and Technology, c. 8, sy. 4, 2018, ss. 271-9, doi:10.21597/jist.412142.
Vancouver Çelik SA. A Two-parameter Deformation of Supergroup GL(1|2). Iğdır Üniv. Fen Bil Enst. Der. 2018;8(4):271-9.

Cited By

Differential Calculi on Super-Hopf Algebra $$\mathsf{F}\varvec{(}{\mathbb {R}}_{\varvec{q}}\varvec{(1|2))}$$ F ( R q ( 1 | 2 ) )
Advances in Applied Clifford Algebras
Sultan Abaci Celik
https://doi.org/10.1007/s00006-018-0903-6