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Subalgebras of free restricted Lie Algebras

Bryant, Roger; Kovacs, L; Stohr, R


A theorem independently due to A.I. Shirshov and E. Witt asserts that every subalgebra of a free Lie algebra (over a field) is free. The main step in Shirshov's proof is a little known but rather remarkable result: if a set of homogeneous elements in a free Lie algebra has the property that no element of it is contained in the subalgebra generated by the other elements, then this subset is a free generating set for the subalgebra it generates. Witt also proved that every subalgebra of a free...[Show more]

CollectionsANU Research Publications
Date published: 2005
Type: Journal article
Source: Bulletin of the Australian Mathematical Society


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