Canonical subgroups of H 1 S L 2 , R

Filippo De Mari; Krzysztof Nowak

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 2, page 405-430
  • ISSN: 0392-4041

Abstract

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We classify, up to conjugation, all subgroups of the semidirect products H 1 S L 2 , R and R 2 S L 2 , R . Our methods can also be applied to all Lie groups that are locally isomorphic to them.

How to cite

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De Mari, Filippo, and Nowak, Krzysztof. "Canonical subgroups of $\mathbb{H}_1\rtimes SL(2,\mathbb{R})$." Bollettino dell'Unione Matematica Italiana 5-B.2 (2002): 405-430. <http://eudml.org/doc/195503>.

@article{DeMari2002,
abstract = {We classify, up to conjugation, all subgroups of the semidirect products $\mathbb\{H\}_1 \rtimes SL(2, \mathbb\{R\})$ and $\mathbb\{R\}^\{2\} \rtimes SL(2, \mathbb\{R\})$. Our methods can also be applied to all Lie groups that are locally isomorphic to them.},
author = {De Mari, Filippo, Nowak, Krzysztof},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {405-430},
publisher = {Unione Matematica Italiana},
title = {Canonical subgroups of $\mathbb\{H\}_1\rtimes SL(2,\mathbb\{R\})$},
url = {http://eudml.org/doc/195503},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - De Mari, Filippo
AU - Nowak, Krzysztof
TI - Canonical subgroups of $\mathbb{H}_1\rtimes SL(2,\mathbb{R})$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/6//
PB - Unione Matematica Italiana
VL - 5-B
IS - 2
SP - 405
EP - 430
AB - We classify, up to conjugation, all subgroups of the semidirect products $\mathbb{H}_1 \rtimes SL(2, \mathbb{R})$ and $\mathbb{R}^{2} \rtimes SL(2, \mathbb{R})$. Our methods can also be applied to all Lie groups that are locally isomorphic to them.
LA - eng
UR - http://eudml.org/doc/195503
ER -

References

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  1. AICARDI, S., La rappresentazione metaplettica estesa, Tesi di Laurea, Genova, 1998. 
  2. DE MARI, F.- NOWAK, K., Reproducing formulae and commutative operator algebras related to affine transformations of the time-frequency plane, Preprint N. 379 bis, Dip. di Matematica, Univ. di Genova1998. 
  3. FOLLAND, G. B., Harmonic Analysis in Phase Space, Princeton University Press, Princeton, 1989. Zbl0682.43001MR983366
  4. LION, G.- VERGNE, M., The Weil representation, Maslov index and Theta series, Birkhäuser, Boston, 1980. Zbl0444.22005MR573448

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