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Title: Novikov structures on solvable Lie algebras
Authors: Burde, Dietrich *
Dekimpe, Karel * # ×
Issue Date: Sep-2006
Publisher: Elsevier science bv
Series Title: Journal of geometry and physics vol:56 issue:9 pages:1837-1855
Abstract: We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable. Conversely we present an example of a nilpotent two-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matfices and via extensions. In the latter case we lift Novikov structures on an abelian Lie algebra a and a Lie algebra b to certain extensions of b by a. We apply this to prove the existence of affine and Novikov structures on several classes of two-step solvable Lie algebras. In particular we generalize a well known result of Scheuneman concerning affine structures on three-step nilpotent Lie algebras. (c) 2005 Elsevier B.V. All rights reserved.
URI: 
ISSN: 0393-0440
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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