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Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2018 / Cilt: 22 - Sayı: 2

A Quantum Space and Some Associated Quantum Groups

Bir Kuantum Uzay ve Bazı ˙Ili¸skili Kuantum Gruplar

Muttalip ÖZAVŞAR
Pages
464–469
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we first introduce a quantum n-space on which the algebraof coordinates is h-commutative.
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Key Findings & Data:Further, it is shown that there are some s-twistedderivations 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 constructedby using s-twisted derivations.
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Conclusion & Impact:Finally, the quantum Lie algebra is obtained by using thisbicovariant differential calculus.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present paper, we first introduce a quantum n-space on which the algebraof coordinates is h-commutative. Further, it is shown that there are some s-twistedderivations 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 constructedby using s-twisted derivations. Finally, the quantum Lie algebra is obtained by using thisbicovariant differential calculus.

Özet

Bu makalede önce koordinatlar cebiri h-de˘gi¸smeli olan bir kuantum uzay tanımlandı. Ayrıca bu cebire etki eden s-bükümlü türevlerin varlı˘gı gösterildi ve bu türevlerin olu¸sturdu˘gu cebirin de˘gi¸smeli ve e¸sde˘gi¸smeli olmayan bir Hopf cebiri oldu˘gu ispat edildi. Üstelik, söz konusu kuantum uzay üzerinde bir bikovaryant diferansiyel hesabın s-bükümlü türevlerin yardımı ile elde edilebilece˘gi gösterildi. En son kuantum Lie cebiri bu diferansiyel hesap yardımı ile olu¸sturuldu.

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Cite This Article

ÖZAVŞAR, M. (2022). 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/654274

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References (13)

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