Products of homogeneous subspaces in free Lie algebras

Stöhr, Ralph and Vaughan-Lee, Michael (2009) Products of homogeneous subspaces in free Lie algebras. International Journal of Algebra and Computation, 19 (5). pp. 699-703. ISSN 0218-1967

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Abstract

Let $L$ be a free Lie algebra of rank $k$ over a field $K$. If $n\geq 1$ then we let $L_n$ denote the homogeneous subspace of $L$ spanned by Lie products of weight $n$ in the free generators of $L$. We obtain formulae for the dimensions of the subspaces $[L_m,L_n]$ for all $m$ and $n$. This answers a question raised by Eamonn O'Brien in private communication.

Item Type: Article
Uncontrolled Keywords: free Lie algebras, homogeneous subspaces, dimension
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User: Prof Ralph Stöhr
Date Deposited: 28 Oct 2009
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1344

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