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

## 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 |
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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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