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Lie algebras graded by the weight systems (Θ3,sl3) and (Θ4,sl4)

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Abstract

A Lie algebra L is said to be (Θn,sln)-graded if it contains a simple subalgebra g isomorphic to sln such that L is generated by g as an ideal and the g-module L decomposes into copies of the adjoint module, the trivial module, the natural module V, its symmetric and exterior squares S2V and , and their duals. In Yaseen (Generalized Root Graded Lie Algebras 2018), Müller et al. (Int Math Res Not IMRN 2010:783–823, 2010), we classified (Θn,sln)-graded Lie algebras for n>4. In this paper we describe the multiplicative structures and the coordinate algebras of (Θn,sln)-graded Lie algebras for n=3,4.

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