论文标题
I型有限的中央扩展
Finite central extensions of type I
论文作者
论文摘要
令$ \ mathbb {g} $为一个谎言组，具有可解决的连接组件和有限生成的组件组，$α\ in H^2（\ Mathbb {g}，\ Mathbb {s}^1）$我们证明，如果$（\ mathbb {g}，α）$是类型I，那么对于$ \ Mathbb {g} $的有限中央扩展也相同。特别是，I型连接的可溶解谎言组的有限中央扩展是I型。这与一般情况相反，因此，I type-I特性在有限的中央扩展下无法生存。 我们还表明，即使不仅连接了后者，也可以在这些连接的可解决的谎言组上进行ad-algebraic船体，并给出了一个连接的，连接的可解决的群体$ \ nathbb {g} $ $ $ n $ $ bb的组的所有欧几里得子组的相互作用的群体理论表征。
Let $\mathbb{G}$ be a Lie group with solvable connected component and finitely-generated component group and $α\in H^2(\mathbb{G},\mathbb{S}^1)$ a cohomology class. We prove that if $(\mathbb{G},α)$ is of type I then the same holds for the finite central extensions of $\mathbb{G}$. In particular, finite central extensions of type-I connected solvable Lie groups are again of type I. This is by contrast with the general case, whereby the type-I property does not survive under finite central extensions. We also show that ad-algebraic hulls of connected solvable Lie groups operate on these even when the latter are not simply connected, and give a group-theoretic characterization of the intersection of all Euclidean subgroups of a connected, simply-connected solvable group $\mathbb{G}$ containing a given central subgroup of $\mathbb{G}$.
