多参数量子超空间及其对数扩张
A Multiparametric Quantum Superspace and Its Logarithmic Extension
摘要：
引入了一个多参数量子超空间，该空间具有$m$偶生成元和$n$奇生成元，它们的对易关系是Manin意义下的，使得相应的代数具有一个Hopf超代数.利用它的Hopf超代数结构，我们给出了一个双协变微分方程及其相关的结构，如Maurer-Cartan型和相应的向量场.还证明了存在与这些矢量场有关的量子超群。此外，我们介绍了这个量子超空间的对数扩展，在这个意义上，我们扩展这个空间的grouplike生成器的对数的级数展开，我们定义了新的元素与非齐次交换关系。可以清楚地看到，这个对数扩张是$κ-$ Minkowski超空间的推广。我们给出了这一扩张上的双共变微分及相关的代数结构。当量子（m+n）-超空间的形变参数为1时，所有的非对易结果都退化为标准超代数的结果.
英文摘要：
We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf superalgebra structure, we give a bicovariant differential calculus and some related structures such as Maurer-Cartan forms and the correspoinding vector fields. It is also shown that there exists a quantum supergroup related with these vector fields. Morever, we introduce the logarithmic extension of this quantum superspace in the sense that we extend this space by the series expansion of the logarithm of the grouplike generator, and we define new elements with nonhomogeneous commutation relations. It is clearly seen that this logarithmic extension is a generalization of the $κ-$Minkowski superspace. We give the bicovariant differential calculus and the related algebraic structures on this extension. All noncommutative results are found to reduce to those of the standard superalgebra when the deformation parameters of the quantum (m+n)-superspace are set to one.
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