The FRT-dual U(O(G_q) \bowtie O(G_q)) and the q-Lorentz Algebra

FRT-duals as Quantum Enveloping Algebras

The Hopf algebra generated by the l-functionals on the quantum double C_q[G] \bowtie C_q[G] is considered, where C_q[G] is the coordinate algebra of a standard quantum group and q is not a root of unity. It is shown to be isomorphic to C_q[G]^op \bowtie U_q(g). This was conjectured by T. Hodges in [Ho]. As an algebra it can be embedded into U_q(g) \otimes U_q(g). Here it is proven that there is no bialgebra structure on U_q(g) \otimes U_q(g), for which this embedding becomes a homomorphism of bialgebras. In particular, it is not an isomorphism. As a preliminary a lemma of [Ho] concerning the s…

量子行列式

Quantum determinants

给出了FRT代数A（R）的中心量子行列式和类群量子行列式的构造方法。作为一般构造的一个应用，我们给出了q-Lorentz群的一个量子行列式。

Sklyanin代数和量子Lorentz群的辫状矩阵结构

Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

辫群和辫矩阵是辫范畴或拟张量范畴中的一类新的代数结构。因此，它们是超群和超矩阵对辫子统计的推广。这里我们构造标准量子群$U_q(g)$的辫群版本。它们有相同的FRT生成元$l^\pm$，但有一个矩阵编织余积$\undΔL=L\und\tens L$，其中$L=l^+Sl^-$，和是自对偶的。作为应用，退化Sklyanin代数被证明与辫子矩阵$BM_q(2)$同构，它是辫子范畴中的辫子交换双代数.作为第二个应用，我们表明，量子双$D(\usl)$（也称为“量子洛伦兹群”）是半直积作为一个代数的两个副本的$\usl$，也是一个半直积作为一个余代数，如果我们使用辫子统计。我们发现了一般量子群的二重群及其半经典极限作为Poisson李群的李代数的二重群的这类结果。