ar X iv : 0 70 5 . 13 16 v 1 [ m at h . R A ] 9 M ay 2 00 7 NOVIKOV ALGEBRAS AND NOVIKOV STRUCTURES ON LIE ALGEBRAS
نویسندگان
چکیده
We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any free three-step nilpotent Lie algebra admits a Novikov structure. We study the existence question also for Lie algebras of triangular matrices. Finally we show that there are families of Lie algebras of arbitrary high solvability class which admit Novikov structures.
منابع مشابه
Novikov Structures on Solvable Lie Algebras
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 2-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matrices and via extensions. In the latter case we lift No...
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