论文标题
与$ gl_n $的drinfeld双重双重的概括集群结构
Generalized Cluster Structures Related to the Drinfeld Double of $GL_n$
论文作者
论文摘要
我们证明，在Arxiv：1912.00453中构建的$ GL_N $的Drinfeld double上的常规群集结构是完整的，并且与Double上的标准泊松结构兼容。此外，我们表明，对于$ n = 4 $，该结构与德林菲尔德双重的先前已知的常规群集结构不同，即使它们具有相同的兼容泊松结构和相同的冷冻变量集合。此外，我们证明了在Arxiv中构建的频段周期矩阵上的常规群集结构：1912.00453具有相似的兼容性和完整性属性。
We prove that the regular generalized cluster structure on the Drinfeld double of $GL_n$ constructed in arXiv:1912.00453 is complete and compatible with the standard Poisson--Lie structure on the double. Moreover, we show that for $n=4$ this structure is distinct from a previously known regular generalized cluster structure on the Drinfeld double, even though they have the same compatible Poisson structure and the same collection of frozen variables. Further, we prove that the regular generalized cluster structure on band periodic matrices constructed in arXiv:1912.00453 possesses similar compatibility and completeness properties.
