A simple proof of the first Kac-Weisfeiler conjecture for algebraic Lie algebras in large characteristics

2018/11/26 by Tikaradze, Akaki
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1811.10182

Abstract

Given a Lie algebra \mathfrakg of an algebraic group over a ring S, we show that the first Kac-Weisfeiler conjecture holds for reductions of \mathfrakg \mod p for large enough primes p, reproving a recent result of Martin, Stewart and Topley. As a byproduct of our proof, we show that the center of the skew field of fractions of the the enveloping algebra \mathfrakU\mathfrakg_k for a field k of characteristic p>>0 is generated by the p-center and by the reduction \mod p of the center of the fraction skew field of \mathfrakU\mathfrakg.

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