Faithful completely reducible representations of modular Lie algebras

2016/03/06 by Barnes, Donald W.
#17B50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1603.01894

Abstract

The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra L over a field F has a finite-dimensional faithful module V. There are several extensions asserting the existence of such a module with various additional properties. In particular, Jacobson has proved that if the field has characteristic p>0, then there exists a completely reducible such module V. I strengthen Jacobson's Theorem, proving that if L has dimension n over the field F of characteristic p>0, then L has a faithful completely reducible module V with dim(V) ≤ p^n2-1.

Related

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