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On Doyle-Grigor’yan criterion for non-parabolicity 论非抛物线的道尔-格里高利准则
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16804
G. Bessa, Vicent Gimeno i Garcia, Leandro Pessoa, Alberto Setti

In this short note we show that Doyle-Grigor’yan criterion for non-parabolicity is not necessary in dimension greater than or equal to four. This gives an negative answer to Problem # 1 of Grigor’yan [Bull. Amer. Math. Soc. (N.S) 36 (1999). pp. 135–249] in this dimensional range.

在这篇短文中，我们证明了在大于或等于四维时，多伊尔-格里高利的非抛物线判据是不必要的。这给出了格里高利问题 #1 [Bull. Amer. Math. Soc. (N.S.) 36 (1999). pp.
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引用次数: 0
Automorphism groups of affine varieties consisting of algebraic elements 代数元素组成的仿射变体的自形群
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16759
Alexander Perepechko, Andriy Regeta
<p>Given an affine algebraic variety <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove that if the neutral component <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal u normal t Superscript ring Baseline left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> <mml:mo>∘<!-- ∘ --></mml:mo> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">mathrm {Aut}^circ (X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earlier result (see Perepechko and Regeta [Transform. Groups 28 (2023), pp. 401–412]). To prove it, we obtain the following fact. If a connected ind-group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains a closed connected nested ind-subgroup <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H subset-of upper G"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">Hsubset G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g element-of upper G"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">gin G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> some positive power of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding="application/x-tex">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> belongs to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.
给定仿射代数簇 X X，我们证明如果自变群的中性分量 A u t ∘ ( X ) mathrm {Aut}^circ (X) 由代数元组成，那么它是嵌套的，即是代数子群的直接极限。这改进了我们之前的结果（见 Perepechko 和 Regeta [Transform. Groups 28 (2023), pp.）为了证明这一点，我们得到以下事实。如果一个连通的吲哚群 G 包含一个封闭的连通嵌套吲哚子群 H ⊂ G Hsubset G ，并且对于任意 g ∈ G gin G，g 的某个正幂次属于 H H ，那么 G = H G=H 。
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引用次数: 0
The prime spectrum of an 𝐿-algebra 𝐿-algebra 的质谱
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16802
Wolfgang Rump, Leandro Vendramin

We prove that the lattice of ideals of an arbitrary L L -algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of L L -algebras and characterize prime ideals in topological terms.

我们证明了任意 L L -代数的理想晶格是可分配的。因此，谱理论的应用不受限制。我们还研究了 L L -代数的谱（即素理想集），并用拓扑术语描述了素理想的特征。
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引用次数: 0
CR embeddings of nilpotent Lie groups 零potent Lie 群的 CR 嵌入
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16818
M. Cowling, M. Ganji, A. Ottazzi, G. Schmalz

In this note we show that a connected, simply connected nilpotent Lie group with an integrable left-invariant complex structure on a generating and suitably complemented subbundle of the tangent bundle admits a Cauchy-Riemann (CR) embedding in complex space defined by polynomials. We also show that a similar conclusion holds on suitable quotients of nilpotent Lie groups. Our results extend the CR embeddings constructed by Naruki [Publ. Res. Inst. Math. Sci. 6 (1970), pp. 113–187] in 1970. In particular, our generalisation to quotients allows us to see a class of Levi degenerate CR manifolds as quotients of nilpotent Lie groups.

在本论文中，我们证明了在切线束的生成子束上具有可积分左不变复结构的简单相连零能李群，在复空间中具有由多项式定义的考奇-黎曼（Cauchy-Riemann，CR）嵌入。我们还证明，类似的结论也适用于零potent Lie 群的适当商。我们的结果扩展了 Naruki [Publ. Res. Inst. Math. Sci.特别是，我们对商的概括使我们能够把一类 Levi 退化 CR 流形看成是无势 Lie 群的商。
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引用次数: 0
Corrigendum to “A Severi type theorem for surfaces in ℙ⁶” 对 "ℙ⁶中曲面的塞维里类型定理 "的更正
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16819
Pietro De Poi, Giovanna Ilardi

In Theorem 0.1 of the paper “A Severi type theorem for surfaces in P 6 mathbb {P}^6 ” [Proc. Amer. Math. Soc. 149 (2021), pp. 591–605], we claimed to have given a complete classification of smooth surfaces in P 6 mathbb {P}^6 with one 4-secant plane through the general point of P 6 mathbb {P}^6 , but the classification is still incomplete.

在论文 "A Severi type theorem for surfaces in P 6 mathbb {P}^6 "[Proc. Amer. Math. Soc. 149 (2021), pp.
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引用次数: 0
Geometry of spectral bounds of curves of unitary operators 单元算子曲线谱边界的几何性质
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16815
Martin Miglioli

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group of unitary operators and the sphere where these operators act.

本文提出了关于单元算子乘积谱边界定理的新证明，以及该定理在可微分曲线上的广义化。证明涉及单元算子组和这些算子作用的球面中的度量几何论证。
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引用次数: 0
The geproci property in positive characteristic 正特征中的 geproci 性质
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16809
Jake Kettinger

The geproci property is a recent development in the world of geometry. We call a set of points Z ⊆ P k 3 Zsubseteq mathbb {P}_k^3 an ( a , b ) (a,b) -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P P to a plane is a complete intersection of curves of degrees a ≤ b aleq b . Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids.

In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.

geproci 属性是几何学领域的最新发展。如果一个点集 Z ⊆ P k 3 Zsubseteq mathbb {P}_k^3 是一个（a , b ）（a,b）-geproci 集（GEneral PROjection is a Complete Intersection 的缩写），而它从一般点 P P 到平面的投影是 a≤b aleq b 的度数的曲线的完全交集，我们就称这个点集为 geproci 集。早在 2011 年，人们就知道了被称为网格的非enerate 例子。2018 年首次描述了非enerate 非网格，在特征 0 下工作。几乎所有这些新例子都属于一种特殊类型，称为半网格。在本文中，我们部分基于作者的论文，利用正特征几何的一个特点，给出了产生geproci半网格和非半网格的新方法。
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引用次数: 0
Spectral stability under removal of small segments 去除小段后的频谱稳定性
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16813
Xiang He

In the present paper, we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Léna on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in R 2 mathbb {R}^2 . We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple.

在本文中，我们深化了 L. Abatangelo、V. Felli、L. Hillairet 和 C. Léna 关于从 R 2 mathbb {R}^2 中的域中移除线段时特征值变化的渐近估计的研究。当特征值简单且移除的线段与相关特征函数的节点线相切时，我们得到了一个尖锐的渐近估计值。此外，我们还将他们的结果扩展到了特征值不简单的情况。
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引用次数: 0
Notes on noncommutative ergodic theorems 非交换遍历定理注释
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16807
Semyon Litvinov

Given a semifinite von Neumann algebra M mathcal M equipped with a faithful normal semifinite trace τ tau , we prove that the spaces L 0 ( M , τ ) L^0(mathcal M,tau ) and R τ mathcal R_tau are complete with respect to pointwise—almost uniform and bilaterally almost uniform—convergences in L 0 ( M , τ ) L^0(mathcal M,tau ) . Then we show that the pointwise Cauchy property for a special class of nets of linear operators in the space L 1 ( M , τ )

给定一个半有穷冯-诺依曼代数 M （M mathcal M）配有一个忠实的正态半有穷迹线 τ tau，我们证明空间 L 0 ( M , τ ) L^0(mathcal M,tau ) 和 R τ mathcal R_tau 就 L 0 ( M , τ ) L^0(mathcal M,tau ) 中的点-几乎均匀和双边几乎均匀-转换而言是完备的。然后，我们证明在空间 L 1 ( M , τ ) L^1(mathcal M., tau ) 中线性算子网的一类特殊的 Pointwise Cauchy 属性可以扩展到 L 0 ( M , τ ) L^0(mathcal M., tau ) 中、tau ) 可以扩展到在任何完全对称空间 E ⊂ R τ Esubset mathcal R_tau 中这类网的点收敛，特别是在任何空间 L p ( M , τ ) L^p(mathcal M,tau ) , 1 ≤ p >；∞ 1leq p>infty .讨论了这些结果在非交换遍历理论中的一些应用。
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引用次数: 0
The Sobol’ sequence is not quasi-uniform in dimension 2 索布尔序列在维 2 中不是准均匀的
IF 1 3区 数学 Q2 MATHEMATICS
Proceedings of the American Mathematical Society
Pub Date : 2024-02-29 DOI: 10.1090/proc/16816
Takashi Goda

Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol’ sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol’ and Shukhman [Math. Comput. Simulation 75 (2007), pp. 80–86] in a negative manner.

常见的准蒙特卡罗序列是准均匀的吗？尽管这个问题仍然悬而未决，但在这篇短文中，我们证明了二维索博尔序列不是准均匀序列。这一结果以否定的方式部分回答了 Sobol' 和 Shukhman [Math. Comput. Simulation 75 (2007), pp.
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引用次数: 0
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