CR-structures on a real Lie algebra

Giuliana Gigante; Giuseppe Tomassini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 3, page 203-205
  • ISSN: 1120-6330

Abstract

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Given the notion of C ⁢ R -structures without torsion on a real 2 ⁢ n + 1 dimensional Lie algebra L 0 we study the problem of their classification when L 0 is a reductive algebra.

How to cite

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Gigante, Giuliana, and Tomassini, Giuseppe. "CR-structures on a real Lie algebra." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.3 (1991): 203-205. <http://eudml.org/doc/244158>.

@article{Gigante1991,
abstract = {Given the notion of \( CR \)-structures without torsion on a real \( 2n + 1 \) dimensional Lie algebra \( \mathcal\{L\}\_\{0\} \) we study the problem of their classification when \( \mathcal\{L\}\_\{0\} \) is a reductive algebra.},
author = {Gigante, Giuliana, Tomassini, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lie algebra; Deformations of special (CR) structures; Analytic moduli problems; -structure; Nijenhuis tensor},
language = {eng},
month = {9},
number = {3},
pages = {203-205},
publisher = {Accademia Nazionale dei Lincei},
title = {CR-structures on a real Lie algebra},
url = {http://eudml.org/doc/244158},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Gigante, Giuliana
AU - Tomassini, Giuseppe
TI - CR-structures on a real Lie algebra
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/9//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 3
SP - 203
EP - 205
AB - Given the notion of \( CR \)-structures without torsion on a real \( 2n + 1 \) dimensional Lie algebra \( \mathcal{L}_{0} \) we study the problem of their classification when \( \mathcal{L}_{0} \) is a reductive algebra.
LA - eng
KW - Lie algebra; Deformations of special (CR) structures; Analytic moduli problems; -structure; Nijenhuis tensor
UR - http://eudml.org/doc/244158
ER -

References

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  1. HELGASON, S., Differential Geometry and Symmetric Spaces. Academic Press, New York1962. Zbl0111.18101MR145455
  2. MALYSEV, F., Complex homogeneous spaces of semisimple Lie groups of the first category. Math. Izvestia, 9, 1975, 939-949. Zbl0338.53036MR402132
  3. SNOW, D., Invariant complex structures on reductive Lie groups. J. für Mathematik, band 371, 1986, 191-215. Zbl0588.22007MR859325DOI10.1515/crll.1986.371.191
  4. SUGIURA, M., Conjugate classes of Cartan subalgebras in real semisimple Lie algebras. J. Math. Soc. Japan, 11, 1959, 375-434. Zbl0204.04201MR146305
  5. WEBSTER, S. M., Pseudo-hermitian structures on a real hypersurface. J. Differential Geometry, 13, 1978, 25-41. Zbl0379.53016MR520599

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