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Lie Powers and Pseudo-Idempotents

Published online by Cambridge University Press:  20 November 2018

Marianne Johnson
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, U.K.e-mail: Marianne.Johnson@maths.manchester.ac.ukRalph.Stohr@manchester.ac.uk
Ralph Stöhr
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, U.K.e-mail: Marianne.Johnson@maths.manchester.ac.ukRalph.Stohr@manchester.ac.uk
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Abstract

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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.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2011

References

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