CR embeddings of nilpotent Lie groups

IF 0.8 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

引用次数: 0

Abstract

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.

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零potent Lie 群的 CR 嵌入

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。

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

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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