Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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 2-step solvable Lie algebras. In
particular we generalize a well known result of Scheuneman concerning affine
structures on 3-step nilpotent Lie algebras.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph