Lie powers and pseudo-idempotents

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

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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.

Item Type: Article
Uncontrolled Keywords: free Lie algebras, idempotents, projections
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Prof Ralph Stöhr
Date Deposited: 04 Aug 2011
Last Modified: 20 Oct 2017 14:12

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