论文标题
单一群体之间的Hodge操作员和异常的异构
Hodge Operators and Exceptional Isomorphisms between Unitary Groups
论文作者
论文摘要
我们将Hodge操作员的概括为空间$（v，h）$赋予了Hermitian或对称的双线性表格$ h $ $ h $，包括任意字段，包括特征性的两个案例。 $ v $的合适外部力量成为使用该操作员定义的代数$ k $的免费模块。这导致了从$ k $的某个子场上合适的形式，从统一团体（相对于$ h $）产生了几种统一团体（相对于$ h $）的几种特殊同态。代数$ k $取决于$ h $;除非$ h $是对称的，并且特征是两个。
We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over an algebra $K$ defined using such an operator. This leads to several exceptional homomorphisms from unitary groups (with respect to $h$) into groups of semi-similitudes with respect to a suitable form over some subfield of $K$. The algebra $K$ depends on $h$; it is a composition algebra unless $h$ is symmetric and the characteristic is two.
