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A construction of modular representations of classical Lie algebras

Authors: Karl M. Peters and Zhiyong Shi
Journal: Proc. Amer. Math. Soc. 122 (1994), 399-407
MSC: Primary 17B10; Secondary 17B50
MathSciNet review: 1233981
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Abstract: In this paper, we construct and analyze new classes of modular representations of classical Lie algebras of type C and type A. These representations include a class of pointed torsion free representations, a class of irreducible nonrestricted representations, and a class of indecomposable representations of arbitrary high dimension. The construction is based on the realization of these Lie algebras in the modular Weyl algebras acting on truncated polynomial algebras. We also classify all the irreducible representations of the modular Weyl algebra.

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