the q-commutators of braided groups
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摘要: 从标准R-矩阵和适当选取的相互对偶的辫子群出发,作者在[1]中利用双重玻色化定理刻画了ABCD型量子包络代数U_q(mathfrakg)的递归构造.本文详细刻画在这些递归构造中,辫子群的生成元在更高一秩的新量子群中的表达式,它们是关于单根向量的q-组合式形式.Abstract: With the standard R-matrices and suitably chosen a pair of dual braided groups, the authors gave the rank-inductive constructions of U_q}(\mathfrakg}}) for the ABCD series via the double-bosonization theory in [1]. This paper described explicitly the expressions for the generators of braided groups in the new higher rank-one quantum groups in these constructions, which are the q-commutators with the simple root vectors. These q-commutators are very important to the structure of new quantum groups.
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[1] [1]HU H M, HU N H. Double-bosonization and Majid's conjecture, (I):rank-induction of $ABCD$ [J/OL]. Journal of Mathematics and Physics,2015, 56(111702); http://dx.doi.org/10.1063/1.4935205.[2] RADFORD D. Hopf algebras with projection[J]. Journal of Algebra,1985, 92(2): 322-347.[3] RADFORD D, TOWBER J. Yetter-Drinfeld categories associated to anarbitrary bialgebra [J]. Journal of Pure and Appl Algebra, 1993,87(3): 259-279.[4] MAJID S. Cross products by braided groups and bosonization [J].Journal of Algebra, 1994, 163(1): 165-190.[5] MAJID S. Some comments on bosonization and biproducts [J]. CzechJournal of Physics, 1997, 47(2): 151-171.[6] MAJID S. Double-bosonization of braided groups and the constructionof U_{q({\mathfrak {g) [J]. Math Proceedings Cambridge PhilosSociety, 1999, 125(1): 151-192.[7] FADDEEV L D, RESHETIKHIN N Y, TAKHTAJAN L A. Quantization of Liegroups and Lie algebras [J]. Leningrad Mathematics J, 1990, 1(1):193--225.[8] DRINFELD V G. Quantum groups [C]//Proceedings of the InternationalCongress of Mathematicians. American Mathematics Society, 1987,1(2): 798-820.[9] LUSZTIG G. Introduction to Quantum Groups [M]. Cambridge, MA: Birkh\"{auser, 1993.[10] KLIMYK A, SCHM\ddot{\rm UDGEN K. Quantum groups and theirrepresentations [M]. Berlin: Springer-Verlag, 1997.[11] MAJID S. Braided momentum in the q-Poincare group. Journal of Mathematics Physics [J]. 1993, 34(5): 2045-2058. -
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