Conformal and CR mappings on Carnot groups
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- by Michael G. Cowling, Ji Li, Alessandro Ottazzi and Qingyan Wu HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 7 (2020), 67-81
Abstract:
We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in $\mathbb {C}^N$ that induce their CR structure.References
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Additional Information
- Michael G. Cowling
- Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
- MR Author ID: 52360
- ORCID: 0000-0003-0995-3054
- Email: m.cowling@unsw.edu.au
- Ji Li
- Affiliation: Department of Mathematics, Macquarie University NSW 2109, Australia
- MR Author ID: 889339
- Email: ji.li@mq.edu.au
- Alessandro Ottazzi
- Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia
- MR Author ID: 762185
- ORCID: 0000-0002-4692-2751
- Email: a.ottazzi@unsw.edu.au
- Qingyan Wu
- Affiliation: Department of Mathematics, Linyi University, Shandong, 276005, People’s Republic of China
- Email: wuqingyan@lyu.edu.cn
- Received by editor(s): November 1, 2019
- Received by editor(s) in revised form: March 13, 2020
- Published electronically: June 17, 2020
- Additional Notes: The first and third authors were supported by the Australian Research Council, through grant DP170103025.
The second author was supported by the Australian Research Council, through grant DP 170101060.
The fourth author was supported by the Natural Science Foundation of China, through Grants 11671185 and 11701250, and by the Natural Science Foundation of Shandong Province, through Grants ZR2018LA002 and ZR2019YQ04. - Communicated by: Jeremy Tyson
- © Copyright 2020 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 7 (2020), 67-81
- MSC (2010): Primary 22E25; Secondary 30L10, 32V15, 35R03, 53C23
- DOI: https://doi.org/10.1090/bproc/48
- MathSciNet review: 4127910