Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras

Alessandro D'Andrea

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 673-686
  • ISSN: 0392-4041

Abstract

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In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.

How to cite

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D'Andrea, Alessandro. "Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 673-686. <http://eudml.org/doc/195501>.

@article{DAndrea2004,
abstract = {In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.},
author = {D'Andrea, Alessandro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {673-686},
publisher = {Unione Matematica Italiana},
title = {Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras},
url = {http://eudml.org/doc/195501},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - D'Andrea, Alessandro
TI - Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 673
EP - 686
AB - In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.
LA - eng
UR - http://eudml.org/doc/195501
ER -

References

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  2. BAKALOV, B.- D'ANDREA, A.- KAC, V. G., Irreducible representations of primitive simple Lie pseudoalgebras, in preparation. 
  3. BEILINSON, A.- DRINFELD, V., Chiral algebras, preprint. MR2058353
  4. CARTAN, E., Les groupes de transformation continus, infinis, simples, Ann. Sci. ENS, 26 (1909), 93-161. MR1509105JFM40.0193.02
  5. D'ANDREA, A.- KAC, V. G., Structure theory of finite conformal algebras, Selecta Math. (N.S.), 4, no. 3 (1998), 377-418. Zbl0918.17019MR1654574
  6. DUBROVIN, B. A.- NOVIKOV, S. P., Poisson brackets of hydrodynamic type (Russian), Dokl. Akad. Nauk SSSR, 279, no. 2 (1984), 294-297. English translation in Soviet Math. Dokl., 30, no. 2 (1984), 651-654. Zbl0591.58012MR770656
  7. DUBROVIN, B. A.- NOVIKOV, S. P., Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory (Russian), Uspekhi Mat. Nauk, 44, no. 6(270) (1989), 29-98, 203. English translation in Russian Math. Surveys, 44, no. 6 (1989), 35-124. Zbl0712.58032MR1037010
  8. GUILLEMIN, V., A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Diff. Geom., 2 (1968), 313-345. Zbl0183.26102MR263882
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  12. KAC, V. G.- RUDAKOV, A. N., Representations of the exceptional Lie superalgebra E ⁢ 3 , 6 . II. Four series of degenerate modules, Comm. Math. Phys.222, no. 3 (2001), 611-661. Zbl0998.17030MR1888090
  13. KOSTRIKIN, I. A., Representations of height 1 of infinite-dimensional Lie algebras of the series K n , (Russian) Uspekhi Mat. Nauk34, no. 1(205) (1979), 229-230. English translation in Russ. Math. Surv., 34, no. 1 (1979), 225-226. Zbl0427.17006MR525661
  14. LAMBEK, J., Deductive systems and categories. II. Standard constructions and closed categories, Lecture Notes in Math., 86, Springer, Berlin, 1969, 76-122. Zbl0198.33701MR242637
  15. RUDAKOV, A. N., Irreducible representations of infinite-dimensional Lie algebras of Cartan type, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 835-866. English transl. in Math. USSR Izv., 8 (1974), 836-866. Zbl0322.17004MR360732
  16. RUDAKOV, A. N., Irreducible representations of infinite-dimensional Lie algebras of types S and H, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 39 (1975), 496-511. English translation in Math. USSR Izv., 9 (1976), 465-480. Zbl0375.17010MR402820
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  18. SOIBELMAN, Y., Meromorphic tensor categories, preprint q-alg/9709030. 

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