Lie algebras graded by the weight system (Θ_n,sl_n)

2017/09/10 by Alexander Baranov, Baranov, Alexander, Hogir Mohammed Yaseen +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1709.03023

openalex publication_date 2017/09/10 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

A Lie algebra L is said to be (Θ_n,sl_n)-graded if it contains a simple subalgebra \mathfrakg isomorphic to sl_n such that the \mathfrakg-module L decomposes into copies of the adjoint module, the trivial module, the natural module V, its symmetric and exterior squares S²V and \wedge²V and their duals. We describe the multiplicative structures and the coordinate algebras of (Θ_n,sl_n)-graded Lie algebras for n≥5, classify these Lie algebras and determine their central extensions.

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