Bir Kuantum Uzay ve Bazı ˙Ili¸skili Kuantum Gruplar

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.

A Quantum Space and Some Associated Quantum Groups

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.

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