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Dergiler / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 22 Sayı: 2

A Quantum Space and Some Associated Quantum Groups

Muttalip Özavşar
Sayfa
464–469
Yayın Tarihi
2018-08-15
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, the quantum Lie algebra is obtained by using this bicovariant differential calculus.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In the present paper, we first introduce a quantum $n$-space on which the algebra of coordinates is $\eta$-commutative.
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Temel Bulgular & Veri:Further, it is shown that there are some $\sigma$-twisted derivations acting on this algebra, and the algebra of such derivations is a quantum group.
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Sonuç & Katkı:Finally, the quantum Lie algebra is obtained by using this bicovariant differential calculus.
🔬Tür:Makale
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Quantum spaces · Quantum groups · Derivation algebras

Özet

In the present paper, we first introduce a quantum $n$-space on which the algebra of coordinates is $\eta$-commutative. Further, it is shown that there are some $\sigma$-twisted derivations acting on this algebra, and the algebra of such derivations is a quantum group. Morever, we show that a bicovariant differential calculus on this space can be constructed by using $\sigma$-twisted derivations. Finally, the quantum Lie algebra is obtained by using this bicovariant differential calculus.

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Bu Makaleye Atıf Yap

Özavşar, M. (2018). A Quantum Space and Some Associated Quantum Groups. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 22 Sayı: 2, 464–469. https://ajindex.com/articles/1312164

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Kaynakça (17)

  1. Drinfeld, VG. 1987, Quantum Groups. Amer. Math. Soc. 1987. Proceedings International Congress of Mathematicians, 03-11 August 1986, Berkeley, 798-820.
  2. Brzezinski, T. 1993. Remark on bicovariant differential calculi and exterior Hopf algebras. Lett Math Phys. 27 (1993), 287-300.
  3. Gurevich, D. Generalized Translation Operators on Lie Groups. Sov J. Cont Math Anal 18 (1983), 57-70.
  4. Borowiec, A., Kharchenko, V. 1995. First order optimum calculi. Bull. Soc. Sci. Lett. L 45(1995), 75-88.
  5. Hu, N. Quantum Divided Power Algebra, QDerivatives, and Some New Quantum Groups. J Algebra 232 (2000), 507-540.
  6. Madore, J. 2000. An Introduction to Noncommutative Differential Geometry and Its Applications. Cambridge, UK: Cambridge University Press.
  7. Majid, S. 1995. Foundation of Quantum Group Theory. Cambridge, UK: Cambridge University Press.
  8. Manin, Y.I. 1988. Quantum Groups and Noncommutative Geometry. Centre de Reserches Mathematiques, Montreal.
  9. Manin, Y.I. 1989. Multiparemetric Quantum Deformation of the General Linear Supergroup. Commu. Math. Phys. 123 (1989), 163-175.
  10. Sudbery, A. 1990. Non-commuting Coordinates and Differential Operators. In Proc.Workshop on Quantum Groups, Argogne, 33-51.
  11. Woronowicz, S.L. 1989. Differential Calculus on Compact Matrix Pseudogroups. Commun. Math. Phys. 122 (1989), 125-170.
  12. Ubriaco, R.M. 1992. Noncommutative Differential Calculus and q-Analysis. J. Phys. A;Math. Gen. 25(1992), 169-173.
  13. Watts, P. Differential Geometry on Hopf Algebras and Quantum Groups, Ph.D. Thesis, hepth/9412153v1.
  14. Wess, J., Zumino, B. 1990. Covariant Differential Calculus on the Quantum Hyperplane. Nucl. Phys. 18(1990), 302-312.
  15. Schüler, A. 1999. Differential Hopf Algebras on Quantum Groups of Type A. J. Algebra 214 (1999), 479-518.
  16. Scheunert, M. 1979. Generalized Lie Algebras. J Math Phys 20 (1979), 712-720.
  17. Scheunert, M. 1979. Generalized Lie Algebras. J Math Phys 20 (1979), 712-720.