关于R-矩阵形式的{ $q$ }-Poincare代数的几点注记
Some remarks on the {$q$}-Poincare algebra in R-matrix form
摘要：
q-变形的辫子方法（由于作者和合作者）给出了自然代数$R_{21}u_1Ru_2=u_2R_{21}u_1R$和$R_{21}x_1x_2=x_2x_1R$分别为q-闵可夫斯基和q-欧几里德空间。这些代数在相应的背景“旋转”量子群下是协变的。半直接产品，这根据玻色化程序（也由于作者）给出了相应的庞加莱量子群。我们回顾了R-矩阵的构造，并收集了欧氏和闵可夫斯基情况下的R-矩阵公式，包括包络代数和函数代数形式，以及它们之间的对偶性。讨论了Poincaré量子群$*$ -结构的公理和Poincaré问题.
英文摘要：
The braided approach to q-deformation (due to the author and collaborators) gives natural algebras $R_{21}u_1Ru_2=u_2R_{21}u_1R$ and $R_{21}x_1x_2=x_2x_1R$ for q-Minkowski and q-Euclidean spaces respectively. These algebras are covariant under a corresponding background `rotation' quantum group. Semidirect product by this according to the bosonisation procedure (also due to the author) gives the corresponding Poincaré quantum groups. We review the construction and collect the resulting R-matrix formulae for both Euclidean and Minkowski cases in both enveloping algebra and function algebra form, and the duality between them. Axioms for the Poincaré quantum group $*$-structure and the dilaton problem are discussed.
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