CR embeddings of nilpotent Lie groups
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- by M. G. Cowling, M. Ganji, A. Ottazzi and G. Schmalz;
- Proc. Amer. Math. Soc. 152 (2024), 3413-3422
- DOI: https://doi.org/10.1090/proc/16818
- Published electronically: June 5, 2024
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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.References
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Bibliographic Information
- M. G. Cowling
- Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney NSW 2052, Australia
- MR Author ID: 52360
- ORCID: 0000-0003-0995-3054
- Email: m.cowling@unsw.edu.au
- M. Ganji
- Affiliation: School of Science and Technology, University of New England, Armidale NSW 2351, Australia
- MR Author ID: 1310246
- ORCID: 0000-0001-6568-6558
- Email: mganjia2@une.edu.au
- A. Ottazzi
- Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney NSW 2052, Australia
- MR Author ID: 762185
- ORCID: 0000-0002-4692-2751
- Email: a.ottazzi@unsw.edu.au
- G. Schmalz
- Affiliation: School of Science and Technology, University of New England, Armidale NSW 2351, Australia
- MR Author ID: 262310
- ORCID: 0000-0002-6141-9329
- Email: schmalz@une.edu.au
- Received by editor(s): December 17, 2023
- Received by editor(s) in revised form: January 14, 2024, and January 17, 2024
- Published electronically: June 5, 2024
- Additional Notes: The first and third-named authors were supported by the Australian Research Council grant DP220100285.
- Communicated by: Harold P. Boas
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 3413-3422
- MSC (2020): Primary 32V15; Secondary 22E25
- DOI: https://doi.org/10.1090/proc/16818
- MathSciNet review: 4767272