Bryant, R. M.
(2002)
*Free Lie algebras and formal power series.*
Journal of Algebra, 253 (1).
pp. 167-188.
ISSN 0021-8669

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## Abstract

Let G be a group and K a field. If V is a graded KG-module of the form V=V1plus sign in circleV2plus sign in circlecdots, three dots, centered , where each Vn is finite dimensional, then the free Lie algebra L(V) acquires the structure of a graded KG-module, L(V)=L1(V)plus sign in circleL2(V)plus sign in circlecdots, three dots, centered . The isomorphism types of V and L(V) may be described by the power series ∑ngt-or-equal, slanted1[Vn]tn and ∑ngt-or-equal, slanted1[Ln(V)]tn with coefficients from the Green ring. The main object of study is the function on power series which maps ∑[Vn]tn to ∑[Ln(V)]tn for every graded KG-module V. Closed formulae are given in certain cases, and these are closely related to character formulae of Brandt and others.

Item Type: | Article |
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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: | Ms Lucy van Russelt |

Date Deposited: | 09 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/474 |

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