BASES, FILTRATIONS AND MODULE DECOMPOSITIONS OF FREE LIE ALGEBRAS

Stöhr, Ralph (2007) BASES, FILTRATIONS AND MODULE DECOMPOSITIONS OF FREE LIE ALGEBRAS. [MIMS Preprint]

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Abstract

We use Lazard Elimination to devise some new bases of the free Lie algebra which (like classical Hall bases) consist of Lie products of left normed basic Lie monomials. Our bases yield direct decompositions of the homogeneous components of the free Lie algebra with direct summands that are particularly easy to describe: they are tensor products of metabelian Lie powers. They also give rise to new filtrations and decompositions of free Lie algebras as modules for groups of graded algebra automorphisms. In particular, we obtain some new decompositions for free Lie algebras and free restricted free Lie algebras over fields of positive characteristic.

Item Type: MIMS Preprint
Uncontrolled Keywords: Free Lie algebras, bases, module decompositions
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User: Prof Ralph Stöhr
Date Deposited: 05 Mar 2007
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/703

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