Polynomial mappings of groups
Polynomial mappings of groups
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DOI：
10.1007/bf02773152
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发表时间：
2002-01-01
影响因子：
1
通讯作者：
Leibman, A
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文献类型：
--
作者：
Leibman, A
群G到群F的映射称为多项式映射，如果它在连续应用算子D-h之后平凡化，h是G的元素，定义为D（h）phi（g）= phi（g）（-1）（gh）.研究群的多项式映射，主要是到幂零群的多项式映射。特别地，我们证明了到幂零群的多项式映射形成一个关于元素乘的群，并且任何到幂零群F的多项式映射G -> F分裂成到幂零群G'的同态G -> G'和多项式映射G' -> F.应用所得结果证明了Hilbert空间在一个非生成幂零群的酉多项式作用下的紧/弱混合分解的存在性.
A mapping phi of a group G to a group F is said to be polynomial if it trivializes after several consecutive applications of operators D-h, h is an element of G, defined by D(h)phi(g) = phi(g)(-1)(gh). We study polynomial mappings of groups, mainly to nilpotent groups. In particular, we prove that polynomial mappings to a nilpotent group form a group with respect to the elementwise multiplication, and that any polynomial mapping G --> F to a nilpotent group F splits into a homomorphism G --> G' to a nilpotent group G' and a polynomial mapping G' --> F. We apply the obtained results to prove the existence of the compact/weak mixing decomposition of a Hilbert space tinder a unitary polynomial action of a finitely generated nilpotent group.