V. L. Popov, “The Jordan Property for Lie Groups and Automorphism Groups of Complex Spaces”, Math. Notes, 103:5 (2018), 811

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Matematicheskie Zametki, 2018, Volume 103, Issue 5, paper published in the English version journal
DOI: https://doi.org/10.1134/S0001434618050139 (Mi mzm12018)

This article is cited in 15 scientific papers (total in 15 papers)

Papers published in the English version of the journal

The Jordan Property for Lie Groups and Automorphism Groups of Complex Spaces

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Citations (15)

DOI: https://doi.org/10.1134/S0001434618050139

Abstract: We prove that the family of all connected

n

$n$ -dimensional real Lie groups is uniformly Jordan for every

n

$n$ . This implies that all algebraic (not necessarily affine) groups over fields of characteristic zero and some transformation groups of complex spaces and Riemannian manifolds are Jordan.

Keywords: Jordan group, bounded group, Lie group, algebraic group, automorphism group of complex space, isometry group of Riemannian manifold.

Funding agency	Grant number
Russian Science Foundation	14-50-00005
This work was carried out at the Steklov Mathematical Institute and supported by the Russian Science Foundation under grant 14-50-00005.

Received: 03.04.2018

English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 811–819
DOI: https://doi.org/10.1134/S0001434618050139

Bibliographic databases:

Document Type: Article

Language: English

Citation: V. L. Popov, “The Jordan Property for Lie Groups and Automorphism Groups of Complex Spaces”, Math. Notes, 103:5 (2018), 811–819

Citation in format AMSBIB

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\by V.~L.~Popov

\paper The Jordan Property for Lie Groups

and Automorphism Groups of Complex Spaces

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\yr 2018

\vol 103

\issue 5

\pages 811--819

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Linking options:

https://www.mathnet.ru/eng/mzm12018

https://doi.org/10.1134/S0001434618050139

Related presentations:

Finite groups of birational selfmaps
K. A. Shramov, November 19, 2018 14:20
Algebraic structure of the Cremona groups and other automorphism groups
V. L. Popov, November 21, 2018 14:15

This publication is cited in the following 15 articles:

Jin Hong Kim, “On the Existence of Equivariant Kähler Models of Certain Compact Complex Spaces”, Math. Notes, 115:4 (2024), 561–568
Tatiana Bandman, Yuri G. Zarhin, “Jordan Groups and Geometric Properties of Manifolds”, Arnold Math J., 2024
A. S. Golota, “Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds”, Sb. Math., 214:1 (2023), 28–38
Russian Math. Surveys, 78:1 (2023), 1–64
A. S. Golota, “Finite groups acting on compact complex parallelizable manifolds”, Int. Math. Res. Not. IMRN, 2023, 1–24
Yu. G. Prokhorov, С. A. Shramov, “Finite groups of bimeromorphic self-maps of nonuniruled Kähler threefolds”, Sb. Math., 213:12 (2022), 1695–1714
Sheng Meng, Fabio Perroni, De‐Qi Zhang, “Jordan property for automorphism groups of compact spaces in Fujiki's class C $\mathcal {C}$ ”, Journal of Topology, 15:2 (2022), 806
M. Sedano-Mendoza, “Isometry groups of generalized stiefel manifolds”, Transformation Groups, 27:4 (2022), 1533
Jin Hong Kim, “Strongly Jordan property and free actions of non-abelian free groups”, Proceedings of the Edinburgh Mathematical Society, 65:3 (2022), 736
Bandman T., Zarhin Yu.G., “Bimeromorphic Automorphism Groups of Certain P-1-Bundles”, Eur. J. Math., 7:2 (2021), 641–670
Yu. Prokhorov, C. Shramov, “Automorphism groups of compact complex surfaces”, Int. Math. Res. Notices, 2021:14 (2021), 10490–10520
Mundet i Riera I., “Isometry Groups of Closed Lorentz 4-Manifolds Are Jordan”, Geod. Dedic., 207:1 (2020), 201–207
S. Kebekus, “Boundedness results for singular fano varieties, and applications to cremona groups [following birkar and prokhorov-shramov]”, Asterisque, 2020, no. 422, 253–290
Yuri G. Zarhin, “Complex Tori, Theta Groups and Their Jordan Properties”, Proc. Steklov Inst. Math., 307 (2019), 22–50
Mundet i Riera I., “Finite group actions on homology spheres and manifolds with nonzero Euler characteristic”, J. Topol., 12:3 (2019), 744–758

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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