Research Article
BibTex RIS Cite

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

Year 2018, , 271 - 279, 30.12.2018

Sultan Abacı Çelik

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

Abstract

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.

Keywords

Yang-Baxter equation super-Hopf algebra quantum supergroup

References

  • 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

Year 2018, , 271 - 279, 30.12.2018

Sultan Abacı Çelik

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

Abstract

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

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

Keywords

Yang-baxter equation super-hopf cebiri kuantum super grup

References

  • 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.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Sultan Abacı Çelik 0000-0003-3465-8209

Publication Date December 30, 2018
Submission Date April 3, 2018
Acceptance Date July 16, 2018
Published in Issue Year 2018

Cite

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. December 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, no. 4 (December 2018): 271-79. https://doi.org/10.21597/jist.412142.
EndNote Çelik SA (December 1, 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., vol. 8, no. 4, pp. 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 (December 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, vol. 8, no. 4, 2018, pp. 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