论文标题
关于布奇斯塔伯 - 介绍“ frobenius $ n $ homorthisms”的理论及其概括
On the Buchstaber--Rees theory of "Frobenius $n$-homomorphisms" and its generalization
论文作者
论文摘要
这是我们对Buchstaber的$ N $ - 肌形态理论的调查及其获得的概括。简而言之，我们关注的是交换环之间的线性图类别，这些线性图可以描述有关乘法性质的“循环同态同态”的“下一级别”。我们的主要工具是一种称为“特征函数”的结构，其功能属性编码了所讨论的线性图的代数属性。也就是说，如果特征函数是$ n $的多项式，那么在Buchstaber的意义上，该地图是$ n $ homormormorm的，而我们的方法可以大大简化其理论。如果特征函数分别与分子和分母分别为$ p $和$ q $的不可约理性分数，那么我们得出了“ $ p | q $ - 肌形态”的新概念。 $ p | q $ - 肌形态的示例是戒指同态的总和和差异。我们的施工是由我们早期的超级/超级几阶结果和超级外部力量的超级几何学的动机。
This is a survey of our results on the theory of $n$-homomorphisms of Buchstaber--Rees and its generalization that we obtained. In short, we are concerned with classes of linear maps between commutative rings that can be described the "next level after ring homomorphisms" with respect to multiplicative properties. Our main tool is a construction which we call the "characteristic function" -- whose functional properties encode algebraic properties of a linear map in question. Namely, if the characteristic function is polynomial of degree $n$, the map is an $n$-homomorphism in the sense of Buchstaber--Rees, and our approach simplifies their theory substantially. If the characteristic function is an irreducible rational fraction with the numerator and denominator of degrees $p$ and $q$ respectively, we arrive at a new notion of a "$p|q$-homomorphism". Examples of $p|q$-homomorphisms are sums and differences of ring homomorphisms. Our construction is motivated by our earlier results in superalgebra/supergeometry concerning Berezinians and super exterior powers.
