A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra

@inproceedings{Durov2006AUF,
title={A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra},
author={Nikolai Durov and Zoran {\vS}koda},
year={2006}
}

Nikolai Durov, Zoran Škoda

Published 2006

Given a n-dimensional Lie algebra g over a field k ⊃ Q, together with its vector space basis X0 1 , . . . ,X 0 n, we give a formula, depending only on the structure constants, representing the infinitesimal generators, Xi = X 0 i t in g ⊗k k[[t]], where t is a formal variable, as a formal power series in t with coefficients in the Weyl algebra An. Actually, the theorem is proved for Lie algebras over arbitrary rings k ⊃ Q. We provide three different proofs, each of which is expected to be… CONTINUE READING