On the modular Plesken Lie algebra
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.14493
- arXiv:
- arXiv:2406.14493
- Bibcode:
- 2024arXiv240614493C
- Keywords:
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- Mathematics - Representation Theory