量子对偶原理
量子代数
2017-06-06 v8
摘要
“量子对偶原理”表述为：一个李双代数通过量子泛包络代数（QUEA）的量化——也通过相伴的形式 Poisson 群——提供其对偶李双代数通过量子形式级数 Hopf 代数（QFSHA）的量化；反之，与一个李双代数（通过其相伴的形式 Poisson 群）相关联的 QFSHA 也给出其对偶李双代数的 QUEA。更确切地说，存在函子 QUEA --> QFSHA 与 QFSHA --> QUEA，互为逆，且在两种情形中目标对象所关联的李双代数均为源对象所关联者的对偶。Drinfeld 曾宣称此结果成立，但文献中似乎未见证明：本文给出其完整详尽的证明。
引用
@article{arxiv.math/9909071,
title = {The quantum duality principle},
author = {Fabio Gavarini},
journal= {arXiv preprint arXiv:math/9909071},
year = {2017}
}
备注
19 pages, AMS-TeX file. The paper has been entirely re-written: in particular, we add a discussion of the possible generalisation of the main result to the infinite dimensional case. This is the author's file of the final version (after the refereeing process), as sent for publication