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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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