Title: Affine structures on 4-step nilpotent Lie algebras
Authors: Dekimpe, Karel * ×
Hartl, M * #
Issue Date: Jul-1997
Publisher: Elsevier science bv
Series Title: Journal of Pure and Applied Algebra vol:120 issue:1 pages:19-37
Abstract: In this paper we construct complete left-symmetric (and so affine) structures on a class of 4-step nilpotent Lie algebras. To achieve this, we use the language of derivations and translate the problem of the existence of a complete left-symmetric structure for a given Lie algebra L, to the existence of a certain submodule (called layerwise complementary) of the augmentation ideal of the universal enveloping algebra of L. A polynomial construction (an analogue of the classical polynomial construction for groups), due to the second author, is used to determine such a submodule for all 3-step nilpotent Lie algebras (allowing to rediscover the known results) and for a reasonable class of 4-step nilpotent Lie algebras (for which the existence of a complete left-symmetric/affine structure was not known before). A concrete description of this left-symmetric structure is given. (C) 1997 Elsevier Science B.V.
ISSN: 0022-4049
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
* (joint) first author
× corresponding author
# (joint) last author

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