论文标题
量子组，离散的马格努斯膨胀，前lie和tridendriform代数
Quantum groups, discrete Magnus expansion, pre-Lie & tridendriform algebras
论文作者
论文摘要
我们将离散的演化问题和相应的解决方案审查为离散的Dyson系列，以便严格地得出Magnus扩展的广义离散版本。我们还系统地得出了前Lie Magnus扩展的离散类似物，并根据Tridendriform代数作用表达离散Dyson系列的元素。在通用的离散情况下，连续或线性离散情况在戴森和马格努斯的扩展中都出现了额外的重要术语。然后，建立基于量子代数，tridendriform和pre-lie代数之间的严格离散派生键连接。这是通过检查量子群（例如扬吉亚语）的张量实现来实现的。我们表明，这些实现可以用tridendriform和lie前代数作用来表达。预期的连续极限提供了扬吉亚人作为前马格努斯膨胀成员的相应非本地电荷。
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 action. 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 actions. The continuous limit as expected provides the corresponding non-local charges of the Yangian as members of the pre-Lie Magnus expansion.
