179 research outputs found

    Generalizations of local bijectivity of Keller maps and a proof of 22-dimensional Jacobian conjecture

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    We give a proof of two-dimensional Jacobian conjecture.Comment: This FINAL version is prepared based on the author's two days' lectures (on May 22, 2022 and May 29,2022; the video of the lectures can be found at https://m.koushare.com/video/videodetail/27869

    Classification of Quasifinite Modules over the Lie Algebras of Weyl Type

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    For a nondegenerate additive subgroup GG of the nn-dimensional vector space FnF^n over an algebraically closed field FF of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type W(G,n)W(G,n) spanned by all differential operators uD1m1...Dnmnu D_1^{m_1}... D_n^{m_n} for u∈F[G]u\in F[G] (the group algebra), and m1,...,mnβ‰₯0m_1,...,m_n \ge 0, where D1,...,DnD_1, ...,D_n are degree operators. In this paper, it is proved that an irreducible quasifinite W(Z,1)W(\Z,1)-module is either a highest or lowest weight module or else a module of the intermediate series; furthermore, a classification of uniformly bounded W(Z,1)W(\Z,1)-modules is completely given. It is also proved that an irreducible quasifinite W(G,n)W(G,n)-module is a module of the intermediate series and a complete classification of quasifinite W(G,n)W(G,n)-modules is also given, if GG is not isomorphic to Z\Z.Comment: 11 pages, LaTe
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