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On the support of irreducible modules over the Witt–Kaplansky algebras of rank (2, 2)

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  26 February 2010

Volodymyr Mazorchuk
Volodymyr Mazorchuk
Affiliation:
Mechanics and Mathematics Department, Kyiv Taras Shevchenko University, 64, Volodymyrska st., 252033, Kyiv, Ukraine
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Abstract

We prove a Futorny-like theorem which describes the support of an irreducible weight module over the Witt–Kaplansky algebra of rank(2, 2).

MSC classification

Secondary: 17B10: Representations, algebraic theory (weights)
Type
Research Article
Information
Mathematika , Volume 45 , Issue 2 , December 1998 , pp. 381 - 389
Copyright
Copyright © University College London 1998

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References

1.Cylke, A., Futorny, V. and Ovsienko, S.. On the support of irreducible modules, SFB-343. Preprint 96-011, Bielefeld, 1996.Google Scholar
2.Futorny, V.. Weight representations of semisimple finite-dimensional Lie algebras. Ph.D. Thesis, Kiev, 1986 (in Russian).Google Scholar
3.Kaplansky, I.. Bull. A MS, 60 (1954), 470– 471.Google Scholar
4.Kawamoto, N.Generalizations of Witt algebra over a field of characteristic zero. Hiroshima Math. J., 16 (1986), 427–441.CrossRefGoogle Scholar
5.Mathieu, O.. Classification of Harish-Chandra modules over the Virasoro Lie algebra. Invent. Math., 107 (192), 225–234.CrossRefGoogle Scholar
6.Mazorchuk, V.. Futorny theorem for generalized Witt algebras of rank 2. Comm. Alg., 25 (2) (1997), 533–541.CrossRefGoogle Scholar
7.Rao, S. Eswara. Irreducible representations of the Lie-algebra of diffeomorphisms of a ci-dimensional torus. J. Algebra, 182 (1996), 401421.CrossRefGoogle Scholar
8.Ree, R.. On generalized Witt algebras. Trans. AMS, 83 (1956), 510–564.CrossRefGoogle Scholar
9.Wilson, R.. Classification of generalized Witt algebras over algebraically closed field. Trans. AMS, 153 (1971). 191210.CrossRefGoogle Scholar