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.