Minimal realizations of classical simple Lie algebras through deformations

Didier Arnal; Hádi Benamor; Benjamin Cahen

Annales de la Faculté des sciences de Toulouse : Mathématiques (1998)

  • Volume: 7, Issue: 2, page 169-184
  • ISSN: 0240-2963

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Arnal, Didier, Benamor, Hádi, and Cahen, Benjamin. "Minimal realizations of classical simple Lie algebras through deformations." Annales de la Faculté des sciences de Toulouse : Mathématiques 7.2 (1998): 169-184. <http://eudml.org/doc/73449>.

@article{Arnal1998,
author = {Arnal, Didier, Benamor, Hádi, Cahen, Benjamin},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {complex simple Lie algebra; star product; mininal realizations},
language = {eng},
number = {2},
pages = {169-184},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Minimal realizations of classical simple Lie algebras through deformations},
url = {http://eudml.org/doc/73449},
volume = {7},
year = {1998},
}

TY - JOUR
AU - Arnal, Didier
AU - Benamor, Hádi
AU - Cahen, Benjamin
TI - Minimal realizations of classical simple Lie algebras through deformations
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1998
PB - UNIVERSITE PAUL SABATIER
VL - 7
IS - 2
SP - 169
EP - 184
LA - eng
KW - complex simple Lie algebra; star product; mininal realizations
UR - http://eudml.org/doc/73449
ER -

References

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  1. [1] Arnal ( D.), Benamor ( H.) and Cahen ( B.) .— Algebraic Deformation Program on Minimal Nilpotent Orbit, Lett. Math. Phys.30 (1994), pp. 241-250. Zbl0805.17009MR1267005
  2. [2] Arnal ( D.) and Cortet ( J.-C.) . — Nilpotent Fourier Transform and Applications, Lett. Math. Phys.9 (1985), pp. 25-34. Zbl0616.46041MR774736
  3. [3] Arnal ( D.) and Cortet ( J.-C.) .- Représentations * des groupes exponentiels, J. of Funct. Anal.92 (1990), pp. 103-135. Zbl0726.22011MR1064689
  4. [4] Arnal ( D.), Cortet ( J.-C.) and Ludwig ( J.) .— Moyal Product and Representations of Solvable Lie Groups, J. of Funct. Anal.133 (1995), pp. 402-424. Zbl0843.22016MR1354037
  5. [5] Bayen ( F.), Flato ( M.), Fronsdal ( C.), Lichnerowicz ( A.) and Sternheimer ( D.) .— Deformation theory and Quantization, Ann. Phys.110 (1978), pp. 61-151. Zbl0377.53024MR496157
  6. [6] Conze ( N.) . — Algèbres d'opérateurs différentiels et quotient des algèbres enveloppantes, Bull. Soc. Math. France102 (1974), pp. 379-415. Zbl0298.17012MR374214
  7. [7] Fronsdal ( C.) .- Some ideas about Quantization, Reports on Math. Phys.15 (1978), pp. 111-145. Zbl0418.58011MR551133
  8. [8] Joseph ( A.) .- Minimal Realizations and Spectrum Generating Algebras, Comm. Math. Phys.36 (1974), pp. 325-338. Zbl0285.17007MR342049
  9. [9] Joseph ( A.) .- The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sci. Ecole Norm. Sup.9 (1976), pp. 1-30. Zbl0346.17008MR404366
  10. [10] Sternberg ( S.) and Wolf ( J.) .- Hermitian Lie algebras and metaplectic representations, Trans. Math. Soc.238 (1978), pp. 1-43. Zbl0386.22010MR486325
  11. [11] Wolf ( J.) . — Representations associated to minimal coadjoint orbits, in Lecture Notes in Math., Springer-Verlarg, New York676 (1978). Zbl0388.22008MR519619
  12. [12] Varadarajan ( V.S.) .- Lie Groups, Lie Algebras and Their Representations, Springer-Verlag, New York (1984). Zbl0955.22500MR746308

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