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2009.41: Products of homogeneous subspaces in free Lie algebras

2009.41: Ralph Stöhr and Michael Vaughan-Lee (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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DOI: 10.1142/S0218196709005287

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 2000 > 17 Nonassociative rings and algebras
MIMS number:2009.41
Deposited By:Prof Ralph Stöhr
Deposited On:28 October 2009

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