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Classification of Simple Harish-Chandra Modules over ℚ-Virasoro Algebra

2000; Wiley; Volume: 209; Issue: 1 Linguagem: Inglês

10.1002/(sici)1522-2616(200001)209

1522-2616

Volodymyr Mazorchuk,

Nonlinear Waves and Solitons

Mathematische NachrichtenVolume 209, Issue 1 p. 171-177 Original Paper Classification of Simple Harish–Chandra Modules over ℚ–Virasoro Algebra Volodymyr Mazorchuk, Volodymyr Mazorchuk mazorchu@uni Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 252033 Kyiv, UkraineSearch for more papers by this author Volodymyr Mazorchuk, Volodymyr Mazorchuk mazorchu@uni Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 252033 Kyiv, UkraineSearch for more papers by this author First published: 20 April 2000 https://doi.org/10.1002/(SICI)1522-2616(200001)209:1 3.0.CO;2-BCitations: 16AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We give a complete classification of simple Harish–Chandra modules over the ℚ–Virasoro algebra. References Andrews, G.: The Theory of Partitions, Addison-Wesley, 1976 Feigin, B., and Fuchs, D.: Representations of the Virasoro Algebra. In: Representations of Lie Groups and Related Topics, Adv. Stud. Cont. Math 7, 447–554, Gordon and Breach, New York, 1990 Futorny, V.: Weight Representations of Semi-Simple Finite-Dimensional Lie Algebras, Ph. D. Thesis, Kiev University, Kiev, 1986 Kawamoto, N.: Generalization of Witt Algebra over a Field of Characteristic Zero, Hiroshima Math. J. 16 (1986), 427–441 Kirkman, E., Procesi, C., and Small, L.: A q-Analog for the Virasoro Algebra, Comm. Alg. 22 (10) (1994), 3755–3774 Martin, C., and Piard, A.: Classification of Indecomposable Bounded Admissible Modules over the Virasoro Lie Algebra with Weight Spaces of Dimension not Exceeding Two, Comm. Math. Phys. 138 (1993), 455–493 Mathieu, O.: Classification of Harish–Chandra Modules over the Virasoro Lie Algebra, Invent. Math. 107 (1992), 225–234 Moody, R., and Pianzola, A.: Lie Algebras with Triangular Decomposition, Canad. Math. Soc. Ser. of Monographs and Adv. Texts, A Wiley-Interscience Publ., New York, 1995 Osborn, J.: New Simple Infinite-Dimensional Lie Algebras of Characteristic 0, J. Algebra 185 (1996), 820–835 Patera, J., and Zassenhaus, H.: The Higher Rank Virasoro Algebras, Comm. Math. Phys. 136 (1991), 1–14 Ree, R.: On Generalized Witt Algebras, Trans. AMS 83 (1956), 510–564 Rocha-Caridi, A., and Wallach, N.: Characters of Irreducible Representations of the Virasoro Algebra, Math. Z. 185 (1984), 1–21 Rocha-Caridi, A., and Wallach, N.: Characters of Irreducible Representations of the Lie Algebra of Vector Fields on the Circle, Invent. Math. 72 (1983), 57–75 Su, Y.: Harish–Chandra Modules of the Intermediate Series over the Higher Rank Virasoro Algebras and Higher Rank Super-Virasoro Algebras, J. Math. Phys. 35 (1994), 2013–2023 Citing Literature Volume209, Issue1January 2000Pages 171-177 ReferencesRelatedInformation