论文标题
古典R-Matrices和Novikov代数
Classical r-matrices and Novikov algebras
论文作者
论文摘要
我们研究了Novikov代数结构在有限维谎言代数上的存在问题。我们表明，一个承认诺维科夫代数的谎言代数必然是可以解决的。相反，我们提出了$ 2 $ step的可解决的谎言代数，而没有任何诺维科夫结构。我们使用扩展名和经典$ r $ - 标准来在某些类似的可解决的LIE代数上构建Novikov结构。
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a $2$-step solvable Lie algebra without any Novikov structure. We use extensions and classical $r$-matrices to construct Novikov structures on certain classes of solvable Lie algebras.
