平面灯夫群不具有负型
Planar lamplighter is not of negative type
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中文总结 AI 辅助
该研究证明平面整数格上的灯夫群不具有负型，不存在到$L_1$的双李普希茨嵌入，揭示有限生成亚阿贝尔群的词度量与CND核的可比性质不被 wreath 积保持。
中文摘要 AI 辅助
已证明，平面整数格上的灯夫群（lamplighter group）不与任何负型度量空间双李普希茨等价，因此特别地，它不存在到$L_1$的双李普希茨嵌入。这表明存在有限生成的亚阿贝尔群，其词度量在常数因子范围内永远不与条件负定（CND）核可比，且允许与词度量可比的CND核的性质不会被 wreath 积保持。
英文摘要
The lamplighter group over the planar integer grid is proved to not be bi-Lipschitz equivalent to any metric space of negative type, so in particular it does not admit a bi-Lipschitz embedding into $L_1$. This shows the existence of finitely generated metabelian groups on which word metrics are never comparable up to constant factors to conditionally negative definite (CND) kernels, and that the property of admitting a word metric-comparable CND kernel is not preserved by wreath products.
