Quantum groups and quantum shuffles
Quantum groups and quantum shuffles
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DOI：
10.1007/s002220050249
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发表时间：
1998-07
影响因子：
3.1
通讯作者：
M. Rosso
中科院分区：
文献类型：
--
作者：
M. Rosso
设Uq+是与可对称化的Cartan矩阵相关联的量化包络代数的“上三角部分”。我们证明了Uq+同构于（作为一个Hopf代数）由余张量Hopf代数的0次和1次元素生成的子代数，该余张量Hopf代数与Zn的群代数上的一个合适的Hopf双模相关联.这种方法给出了超对称以及多参数版本的Uq+在一个统一的方式（一个合适的选择的霍普夫双模）。在适当的增长条件下，给出了用这种方法得到的Hopf代数的一个分类结果。我们还展示了一般形式如何允许从Uqsl（2）和一个合适的不可约有限维表示重建更高秩的量子化包络代数。
LetUq+be the “upper triangular part” of the quantized enveloping algebra associated with a symetrizable Cartan matrix. We show thatUq+is isomorphic (as a Hopf algebra) to the subalgebra generated by elements of degree 0 and 1 of the cotensor Hopf algebra associated with a suitable Hopf bimodule on the group algebra ofZn. This method gives supersymetric as well as multiparametric versions ofUq+in a uniform way (for a suitable choice of the Hopf bimodule). We give a classification result about the Hopf algebras which can be obtained in this way, under a reasonable growth condition. We also show how the general formalism allows to reconstruct higher rank quantized enveloping algebras fromUqsl(2) and a suitable irreducible finite dimensional representation.