论文标题
$ \ mathfrak {sl} _ {2}（\ mathbb {r}）$ calgebra对称和可整合的离散时间系统
The $\mathfrak{sl}_{2}(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems
论文作者
论文摘要
在本文中，我们以$ n $ n $ n $ n $ n $ n $自由度对所有变异离散时间系统进行了分类，以实现lie-poisson algebra $ \ mathfrak {sl} {sl} _ {2} _ {2}（\ mathbb {r}）$的lie-poisson algebra $ \ mathfrak $ \ mathfrak $ \ mathfrak $ \ mathfrak $ n $ n $程度。这种方法自然会产生几种超值和最大促进的离散时间系统，包括已知和新的系统。我们猜想这会耗尽与该代数结构相关的（超级）综合案例。
In this paper, we classify all the variational discrete-time systems in quasi-standard form in $N$ degrees of freedom admitting coalgebra symmetry with respect to the generic realisation of the Lie-Poisson algebra $\mathfrak{sl}_{2}(\mathbb{R})$. This approach naturally yields several quasi-maximally and maximally superintegrable discrete-time systems, both known and new. We conjecture that this exhausts the (super)integrable cases associated with this algebraic construction.
