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D'Andrea, Alessandro:
Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras
Bollettino dell'Unione Matematica Italiana Serie 8 7-B (2004), fasc. n.3, p. 673-686, Unione Matematica Italiana (English)
pdf (263 Kb), djvu (179 Kb). | MR2101658 | Zbl 1114.17010

Sunto

In questa comunicazione, elenco i principali risultati [BDK1] di classificazione delle pseudoalgebre di Lie finite, che generalizzano diverse strutture algebriche precedentemente note, e annuncio alcuni nuovi risultati [BDK2] che riguardano le loro rappresentazioni.
Referenze Bibliografiche
[BDK1] B. BAKALOV-A. D'ANDREA-V. G. KAC, Theory of finite pseudoalgebras, Adv. Math., 162 (2001), 1-140. | MR 1849687 | Zbl 1001.16021
[BDK2] B. BAKALOV-A. D'ANDREA-V. G. KAC, Irreducible representations of primitive simple Lie pseudoalgebras, in preparation.
[BeDr] A. BEILINSON-V. DRINFELD, Chiral algebras, preprint. | MR 2058353
[Ca] E. CARTAN, Les groupes de transformation continus, infinis, simples, Ann. Sci. ENS, 26 (1909), 93-161. | fulltext mini-dml | MR 1509105 | Jbk 40.0193.02
[DK] A. D'ANDREA-V. G. KAC, Structure theory of finite conformal algebras, Selecta Math. (N.S.), 4, no. 3 (1998), 377-418. | MR 1654574 | Zbl 0918.17019
[DuN1] B. A. DUBROVIN-S. P. NOVIKOV, 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. | MR 770656 | Zbl 0591.58012
[DuN2] B. A. DUBROVIN-S. P. NOVIKOV, 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. | MR 1037010 | Zbl 0712.58032
[Gu1] V. GUILLEMIN, A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras, J. Diff. Geom., 2 (1968), 313-345. | fulltext mini-dml | MR 263882 | Zbl 0183.26102
[Gu2] V. GUILLEMIN, Infinite-dimensional primitive Lie algebras, J. Diff. Geom., 4 (1970), 257-282. | fulltext mini-dml | MR 268233 | Zbl 0223.17007
[K] V. G. KAC, Vertex algebras for beginners, University Lecture Series, 10. American Mathematical Society, Providence, RI, 1996. Second edition 1998. | MR 1651389 | Zbl 0861.17017
[KRud1] V. G. KAC-A. N. RUDAKOV, Representations of the exceptional Lie superalgebra $E(3, 6)$. I. Degeneracy conditions, Transform. Groups, 7, no. 1 (2002), 67-86. | MR 1888477 | Zbl 0997.17005
[KRud2] V. G. KAC-A. N. RUDAKOV, Representations of the exceptional Lie superalgebra $E(3, 6)$. II. Four series of degenerate modules, Comm. Math. Phys. 222, no. 3 (2001), 611-661. | MR 1888090 | Zbl 0998.17030
[Ko] I. A. KOSTRIKIN, Representations of height 1 of infinite-dimensional Lie algebras of the series $K_n$, (Russian) Uspekhi Mat. Nauk 34, no. 1(205) (1979), 229-230. English translation in Russ. Math. Surv., 34, no. 1 (1979), 225-226. | MR 525661 | Zbl 0427.17006
[L] J. LAMBEK, Deductive systems and categories. II. Standard constructions and closed categories, Lecture Notes in Math., 86, Springer, Berlin, 1969, 76-122. | MR 242637 | Zbl 0198.33701
[Rud1] A. N. RUDAKOV, 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. | MR 360732 | Zbl 0322.17004
[Rud2] A. N. RUDAKOV, 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. | MR 402820 | Zbl 0375.17010
[Rum] M. RUMIN, Formes différentielles sur les variétés de contact, (French) J. Diff. Geom., 39 (1994), 281-330. | fulltext mini-dml | MR 1267892 | Zbl 0973.53524
[So] Y. SOIBELMAN, Meromorphic tensor categories, preprint q-alg/9709030. | fulltext mini-dml

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