量子群、离散马格努斯展开、前李代数和三叶代数
Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras
AI总结：
本文通过离散戴森级数和三叶代数，推导了量子群与前李代数之间的联系，并揭示了离散马格努斯展开的结构。
摘要：
我们回顾了离散演化的問題及其对应的解作为离散戴森级数，以严谨地推导出广义的离散马格努斯展开的版本。我们还系统地推导出前李马格努斯展开的离散类比，并将离散戴森级数的元素用三叶代数二元运算表达。在一般的离散情况下，戴森和马格努斯展开中会出现额外的重要项，这些项在连续或线性离散情况下是不存在的。基于严谨的离散推导，建立了量子代数、三叶代数和前李代数之间的关键联系。这通过检查量子群的张量表示，如Yangian来实现。我们展示这些表示可以表示为三叶代数和前李代数。连续极限如预期提供Yangian的相应非本地荷作为前李马格努斯展开的成员。
英文摘要：
We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and express the elements of the discrete Dyson series in terms of a tridendriform algebra binary operation. In the generic discrete case, extra significant terms that are absent in the continuous or the linear discrete case appear in both Dyson and Magnus expansions. Based on the rigorous discrete derivation key links between quantum algebras, tridendriform and pre-Lie algebras are then established. This is achieved by examining tensor realizations of quantum groups, such as the Yangian. We show that these realizations can be expressed in terms of tridendriform and pre-Lie algebras. The continuous limit as expected provides the corresponding non-local charges of the Yangian as members of the pre-Lie Magnus expansion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
