Representations of four-derivation Lie algebras of Block type |
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Authors: | Yu Feng Zhao Zhi Bin Liang |
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Institution: | 1. LAMA, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China 2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China
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Abstract: | Block introduced certain analogues of the Zassenhaus algebras over a field of characteristic 0. The nongraded infinite-dimensional
simple Lie algebras of Block type constructed by Xu can be viewed as generalizations of the Block algebras. In this paper,
we construct a family of irreducible modules in terms of multiplication and differentiation operators on “polynomials” for
four-devivation nongraded Lie algebras of Block type based on the finite-dimensional irreducible weight modules with multiplicity
one of general linear Lie algebras. We also find a new series of submodules from which some irreducible quotient modules are
obtained. |
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Keywords: | irreducible modules nongraded Lie algebras nongraded Lie algebras of Block type |
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