A substitute for Kazhdan’s property (T) for universal nonlattices

IF 1.8 1区 数学 Q1 MATHEMATICS Analysis & PDE Pub Date : 2024-08-21 DOI:10.2140/apde.2024.17.2541
Narutaka Ozawa
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引用次数: 0

Abstract

The well-known theorem of Shalom–Vaserstein and Ershov–Jaikin-Zapirain states that the group EL n(), generated by elementary matrices over a finitely generated commutative ring , has Kazhdan’s property (T) as soon as n 3. This is no longer true if the ring is replaced by a commutative rng (a ring but without the identity) due to nilpotent quotients EL n(k). We prove that even in such a case the group EL n() satisfies a certain property that can substitute property (T), provided that n is large enough.

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卡兹丹性质 (T) 在通用非网格中的替代物
沙洛姆-瓦瑟斯坦和埃尔绍夫-杰金-扎皮林的著名定理指出,由有限生成交换环ℛ上的基本矩阵生成的群 EL n(ℛ) 只要 n≥ 3 就具有卡兹丹性质 (T)。如果由于无穷商 EL n(ℛ∕ℛk) 的原因,把环ℛ 换成了交换环 rng(一个环,但没有同一性),那么上述性质就不再成立了。我们将证明,即使在这种情况下,只要 n 足够大,EL n(ℛ)群也能满足某个可以替代性质 (T) 的性质。
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来源期刊
Analysis & PDE
Analysis & PDE MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.80
自引率
0.00%
发文量
38
审稿时长
6 months
期刊介绍: APDE aims to be the leading specialized scholarly publication in mathematical analysis. The full editorial board votes on all articles, accounting for the journal’s exceptionally high standard and ensuring its broad profile.
期刊最新文献
Uniform Skoda integrability and Calabi–Yau degeneration Unique continuation for the heat operator with potentials in weak spaces Nonnegative Ricci curvature and minimal graphs with linear growth Haagerup’s phase transition at polydisc slicing A substitute for Kazhdan’s property (T) for universal nonlattices
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