A Quantum Space and Some Associated Quantum Groups

Muttalip Özavşar

A Quantum Space and Some Associated Quantum Groups

Abstract

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.

Keywords

Quantum spaces,Quantum groups; Derivation algebras

References

[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.

Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Muttalip Özavşar This is me

Publication Date

August 15, 2018

Submission Date

May 12, 2017

Acceptance Date

-

Published in Issue

Year 2018 Volume: 22 Number: 2

IZ

https://izlik.org/JA23HX89WC

Cite

RIS / Bibtex

APA

Özavşar, M. (2018). A Quantum Space and Some Associated Quantum Groups. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 464-469. https://izlik.org/JA23HX89WC

AMA

1.Özavşar M. A Quantum Space and Some Associated Quantum Groups. J. Nat. Appl. Sci. 2018;22(2):464-469. https://izlik.org/JA23HX89WC

Chicago

Özavşar, Muttalip. 2018. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2): 464-69. https://izlik.org/JA23HX89WC.

EndNote

Özavşar M (August 1, 2018) A Quantum Space and Some Associated Quantum Groups. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 464–469.

IEEE

[1]M. Özavşar, “A Quantum Space and Some Associated Quantum Groups”, J. Nat. Appl. Sci., vol. 22, no. 2, pp. 464–469, Aug. 2018, [Online]. Available: https://izlik.org/JA23HX89WC

ISNAD

Özavşar, Muttalip. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (August 1, 2018): 464-469. https://izlik.org/JA23HX89WC.

JAMA

1.Özavşar M. A Quantum Space and Some Associated Quantum Groups. J. Nat. Appl. Sci. 2018;22:464–469.

MLA

Özavşar, Muttalip. “A Quantum Space and Some Associated Quantum Groups”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, Aug. 2018, pp. 464-9, https://izlik.org/JA23HX89WC.

Vancouver

1.Muttalip Özavşar. A Quantum Space and Some Associated Quantum Groups. J. Nat. Appl. Sci. [Internet]. 2018 Aug. 1;22(2):464-9. Available from: https://izlik.org/JA23HX89WC