论文标题
在基于超级plücker和超级托勒密关系的超级集群代数上
On super cluster algebras based on super Plücker and super Ptolemy relations
论文作者
论文摘要
我们研究了超级Plücker和Super托勒密关系提供的示例中产生的超集群代数结构。我们为任意$ n $开发了超级草曼尼亚人的超级集群结构$ \ gr_ {2 | 0}（n | 1）$，这在我们与Th的联合合作中较早表示。 Voronov。对于Penner-Zeitlin装饰的SuperTeichmüller空间的超级托勒密关系，我们展示了如何通过变量的更改将其转变为古典托勒密关系，而新的偶数变量与奇数变量解耦合。我们还为一般超级格拉斯曼尼亚人分析了超级plücker关系，并为$ \ gr_ {r | 1}（n | 1）$获得了一种新的简单关系形式。为此，我们建立了某些类型矩阵的Berezinians的属性（我们称为“错误”）。
We study super cluster algebra structure arising in examples provided by super Plücker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannians $\Gr_{2|0}(n|1)$ for arbitrary $n$, which was indicated earlier in our joint work with Th. Voronov. For the super Ptolemy relation for the decorated super Teichmüller space of Penner-Zeitlin, we show how by a change of variables it can be transformed into the classical Ptolemy relation with the new even variables decoupled from odd variables. We also analyze super Plücker relations for general super Grassmannians and obtain a new simple form of the relations for $\Gr_{r|1}(n|1)$. To this end, we establish properties of Berezinians of certain type matrices (which we call ``wrong'').
