Lattices in $$\mathbb {R}^n\rtimes \textrm{SL}_2(\mathbb {R})$$

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2024-08-07 DOI:10.1007/s00031-024-09874-z

M. M. Radhika, Sandip Singh

引用次数: 0

Abstract

We determine the existence of cocompact lattices in groups of the form $\textrm{V}\rtimes \textrm{SL}_2(\mathbb {R})$, where $\textrm{V}$ is a finite dimensional real representation of $\textrm{SL}_2(\mathbb {R})$. It turns out that the answer depends on the parity of $\dim (\textrm{V})$ when the representation is irreducible.

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在 $$\mathbb {R}^n\rtimes \textrm{SL}_2(\mathbb {R})$$ 中的网格

我们确定了在$\textrm{V}\rtimes \textrm{SL}_2(\mathbb {R})$形式的群中cocompact网格的存在性，其中$\textrm{V}$是$\textrm{SL}_2(\mathbb {R})$的有限维实数表示。事实证明，当表示是不可还原的时候，答案取决于 $\dim (\textrm{V})$ 的奇偶性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.