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2008.57: Lie powers and pseudo-idempotents

2008.57: Marianne Johnson and Ralph Stöhr (2011) Lie powers and pseudo-idempotents. Canadian Mathematical Bulletin, 54 (2). pp. 297-301. ISSN 0008-4395

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DOI: 10.4153/CMB-2011-014-x

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.

Item Type:Article
Uncontrolled Keywords:free Lie algebras, idempotents, projections
Subjects:MSC 2000 > 17 Nonassociative rings and algebras
MSC 2000 > 20 Group theory and generalizations
MIMS number:2008.57
Deposited By:Prof Ralph Stöhr
Deposited On:04 August 2011

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