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20 April 2024

» arxiv » 1706.0534

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On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component
Thomas B. Gregory ; Michael I. Kuznetsov ;
Date:	2 Jun 2017
Abstract:	We consider finite-dimensional irreducible transitive graded Lie algebras $L = sum_{i=-q}^rL_i$ over algebraically closed fields of characteristic three. We assume that the null component $L_0$ is classical and reductive. The adjoint representation of $L$ on itself induces a representation of the commutator subalgebra $L_0’$ of the null component on the minus-one component $L_{-1}.$ We show that if the depth $q$ of $L$ is greater than one, then this representation must be restricted.
Source:	arXiv, 1706.0534
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