对偶性的代数学方法：导论
The Algebraic Approach to Duality: An Introduction
摘要：
本文对马尔可夫过程对偶性的代数方法作了初步的介绍。在代数方法中，马尔可夫生成元被写为简单算子的乘积之和，每个算子都有关于某个对偶函数的对偶。我们详细讨论了Giardinà、Redig和其他人最近提出的建议，即选择这些简单的算子，使它们形成某些已知李代数的不可约表示，可能是一个好主意。特别是，我们收集的李代数，这是至关重要的这种方法表示必要的背景。我们还讨论了劳埃德和萨德伯里关于产品形式的对偶函数以及交织和对偶之间的关系的旧工作。
英文摘要：
This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise approach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent suggestion by Giardinà, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations of Lie algebras that is crucial for this approach. We also discuss older work by Lloyd and Sudbury on duality functions of product form and the relation between intertwining and duality.
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。
