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arXiv · 2406.14493

On the modular Plesken Lie algebra

John Cullinan
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Abstract

Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the complex group algebra C[G] and admits a direct-sum decomposition into simple Lie algebras based on the ordinary character theory of G. In this paper we review the known results on L[G] and related Lie algebras, as well as introduce a conjecture on a characteristic p analog L_p[G], with a focus on when p divides the order of G.

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John Cullinan. 2024-06-20. On the modular Plesken Lie algebra. https://arxiv.org/abs/2406.14493

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