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Central Series for Groups with Action and Leibniz Algebras

Central Series for Groups with Action and Leibniz Algebras The notion of central series for groups with action on itself is introduced. An analogue of Witt's construction is given for such groups. A certain condition is found for the action and the corresponding category is defined. It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restriction of this functor on the category of groups leads us to Lie algebras and gives the result of Witt. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Central Series for Groups with Action and Leibniz Algebras

Georgian Mathematical Journal , Volume 9 (4) – Dec 1, 2002

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References (9)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2002.671
Publisher site
See Article on Publisher Site

Abstract

The notion of central series for groups with action on itself is introduced. An analogue of Witt's construction is given for such groups. A certain condition is found for the action and the corresponding category is defined. It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restriction of this functor on the category of groups leads us to Lie algebras and gives the result of Witt.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2002

Keywords: Central series; groups; groups with action on itself; Lie algebras; Leibniz algebras; Lie–Leibniz algebras

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