论文标题
替代卡兹丹财产（T）代替通用非企业
A substitute for Kazhdan's property (T) for universal non-lattices
论文作者
论文摘要
The well-known theorem of Shalom--Vaserstein and Ershov--Jaikin-Zapirain states that the group $\mathrm{EL}_n(\mathcal{R})$, generated by elementary matrices over a finitely generated commutative ring $\mathcal{R}$, has Kazhdan's property (T) as soon as $n\geq3$.如果戒指$ \ mathcal {r} $被通勤的RNG（戒指但没有身份）代替，这是不再正确的，因为nilpotent的商$ \ mathrm {el} _n（\ MathCal {r}/\ Mathcal {r}/\ Mathcal {r}^k）$。在本文中，我们证明，即使在这种情况下，只要$ n $就足够大，就可以满足一个可以替换属性（t）的特定属性（t）$ \ mathrm {el} _n（\ mathcal {r}）$。
The well-known theorem of Shalom--Vaserstein and Ershov--Jaikin-Zapirain states that the group $\mathrm{EL}_n(\mathcal{R})$, generated by elementary matrices over a finitely generated commutative ring $\mathcal{R}$, has Kazhdan's property (T) as soon as $n\geq3$. This is no longer true if the ring $\mathcal{R}$ is replaced by a commutative rng (a ring but without the identity) due to nilpotent quotients $\mathrm{EL}_n(\mathcal{R}/\mathcal{R}^k)$. In this paper, we prove that even in such a case the group $\mathrm{EL}_n(\mathcal{R})$ satisfies a certain property that can substitute property (T), provided that $n$ is large enough.
