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- W2078547515 abstract "Let g ( A ) be the modular classical Lie algebra over an algebraically closed field k of characteristic p > 0, defined by a Cartan matrix A and Serre′s relations and generators E i , H i , F i . A representation V of g ( A ) is called weak torsion free if the generators E i , F i act injectively on V and is called pointed if V is irreducible and has a one dimensional weight space. In this paper assuming p > 3 and A ≠ A ip − 1 , we classify for all indecomposable Cartan matrices A the pointed (weak) torsion free representations of g ( A ) up to isomorphism. It turns out to be the only g ( A ) for A of type A l ( p [formula] l + 1) and C l , admit pointed (weak) torsion free representations. Explicit constructions of these representations are given by specifying actions of generators E i , F i , H i on a chosen basis. Also all these pointed weak torsion free representations are realized by differential operators through the modular Weyl algebras." @default.
- W2078547515 created "2016-06-24" @default.
- W2078547515 creator A5061449087 @default.
- W2078547515 date "1995-02-01" @default.
- W2078547515 modified "2023-10-14" @default.
- W2078547515 title "Classification of Pointed Weak Torsion Free Representations for Classical Lie Algebras" @default.
- W2078547515 doi "https://doi.org/10.1006/jabr.1995.1033" @default.
- W2078547515 hasPublicationYear "1995" @default.
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