群的动物学：儿童的死亡，有限几何和量子交换
Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation
摘要：
每个有限单群P都可以由它的两个元素生成。P的生成元对可以在有限群表示的图集中作为（不一定是最小的）置换表示P获得。认识到P是Grothendieck's dessin d 'enfant D并且大多数标准图和有限几何G--例如近似多边形及其推广--被D稳定化是不寻常的但重要的。在我们的论文中，三脚架P - D - G的秩大于2，对应于简单的群体，被组织成类，例如辛，酉，零星等（如在地图集）。一个详尽的搜索和表征的非平凡的点线配置定义从简单的群的小指数表示，其目标是认识到它们的量子物理意义。所有定义的几何形状G都具有接近其最大值1的上下文参数。
英文摘要：
Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck's dessin d'enfant D and that most standard graphs and finite geometries G-such as near polygons and their generalizations-are stabilized by a D. In our paper, tripods P -- D -- G of rank larger than two, corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G' s have a contextuality parameter close to its maximal value 1.
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