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# Lie Powers and Pseudo-Idempotents

Published:2011-02-10
Printed: Jun 2011
• Marianne Johnson,
School of Mathematics, University of Manchester, Manchester, M13 9PL, U.K.
• Ralph Stöhr,
School of Mathematics, University of Manchester, Manchester, M13 9PL, U.K.
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## Abstract

We give a new factorisation of the classical Dynkin operator, an element of the integral group ring of the symmetric group that facilitates projections of tensor powers onto Lie powers. As an application we show that the iterated Lie power $L_2(L_n)$ is a module direct summand of the Lie power $L_{2n}$ whenever the characteristic of the ground field does not divide $n$. An explicit projection of the latter onto the former is exhibited in this case.
 MSC Classifications: 17B01 - Identities, free Lie (super)algebras 20C30 - Representations of finite symmetric groups

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