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A Quantum Space and Some Associated Quantum Groups

Yıl 2018, Cilt: 22 Sayı: 2, 464 - 469, 15.08.2018

Muttalip Özavşar

Öz

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.

Anahtar Kelimeler

Quantum spaces Quantum groups; Derivation algebras

Kaynakça

  • [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 .
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Muttalip Özavşar Bu kişi benim

Yayımlanma Tarihi 15 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 2

Kaynak Göster

APA Özavşar, M. (2018). A Quantum Space and Some Associated Quantum Groups. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 464-469.
AMA Özavşar M. A Quantum Space and Some Associated Quantum Groups. SDÜ Fen Bil Enst Der. Ağustos 2018;22(2):464-469.
Chicago Özavşar, Muttalip. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, sy. 2 (Ağustos 2018): 464-69.
EndNote Özavşar M (01 Ağustos 2018) A Quantum Space and Some Associated Quantum Groups. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 464–469.
IEEE M. Özavşar, “A Quantum Space and Some Associated Quantum Groups”, SDÜ Fen Bil Enst Der, c. 22, sy. 2, ss. 464–469, 2018.
ISNAD Özavşar, Muttalip. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (Ağustos 2018), 464-469.
JAMA Özavşar M. A Quantum Space and Some Associated Quantum Groups. SDÜ Fen Bil Enst Der. 2018;22:464–469.
MLA Özavşar, Muttalip. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 22, sy. 2, 2018, ss. 464-9.
Vancouver Özavşar M. A Quantum Space and Some Associated Quantum Groups. SDÜ Fen Bil Enst Der. 2018;22(2):464-9.
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