Classification of quasifinite W∞-modules 1
نویسنده
چکیده
It is proved that an irreducible quasifinite W∞-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight W∞module is a module of the intermediate series. For a nondegenerate additive subgroup Γ of F, where F is a field of characteristic zero, there is a simple Lie or associative algebra W(Γ, n)(1) spanned by differential operators uD1 1 · · ·D mn n for u ∈ F[Γ] (the group algebra), and mi ≥ 0 with ∑n i=1 mi ≥ 1, where Di are degree operators. It is also proved that an indecomposable quasifinite weight W(Γ, n)(1)-module is a module of the intermediate series if Γ is not isomorphic to Z. Mathematics Subject Classification (1991): 17B10, 17B65, 17B66, 17B68
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3 A pr 2 00 3 Classification of Quasifinite Modules over the Lie Algebras of Weyl Type
For a nondegenerate additive subgroup Γ of the n-dimensional vector space IF over an algebraically closed field IF of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type W(Γ, n) spanned by all differential operators uD1 1 · · ·D mn n for u ∈ IF [Γ] (the group algebra), and m1, ...,mn ≥ 0, where D1, ...,Dn are degree operators. In this paper, it is proved that an ...
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