Finite dimensional Lie algebras are semi-direct product of the semi-simple Lie algebras and solvable Lie algebras. Brieskorn gave the connection between simple Lie algebras and simple singularities. Simple Lie algebras have been well understood, but not the solvable (nilpotent) Lie algebras. It is extremely important to establish connections between singularities and solvable (nilpotent) Lie algebras. In this article, a new natural connection between the set of complex analytic isolated hypersurface singularities and the set of finite dimensional solvable (nilpotent) Lie algebras has been constructed. We construct finite dimensional solvable (nilpotent) Lie algebras naturally from isolated hypersurface singularities. These constructions help us to understand the solvable (nilpotent) Lie algebras from the geometric point of view. Moreover, it is known that the classification of nilpotent Lie algebras in higher dimensions ($\gt 7$) remains to be a vast open area. There are one-parameter families of non-isomorphic nilpotent Lie algebras (but no two-parameter families) in dimension seven. Dimension seven is the watershed of the existence of such families. It is well-known that no such family exists in dimension less than seven, while it is hard to construct one-parameter family in dimension greater than seven. In this article, we construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension $11$ (resp. $10$) from $\tilde{E}_7$ singularities and show that the weak Torelli-type theorem holds. We shall also construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension $12$ (resp. $11$) from $\tilde{E}_8$ singularities and show that the Torelli-type theorem holds. Moreover, we investigate the numerical relation between the dimensions of the new Lie algebras and Yau algebras. Finally, the new Lie algebras arising from fewnomial isolated singularities are also computed.

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复杂结构的变化和李代数的变化II：奇点产生的新李代数

有限维李代数是半简单李代数和可解李代数的半直接乘积。Brieskorn给出了简单李代数和简单奇点之间的联系。简单的李代数已经广为人知，但可解（幂等）李代数却不是。在奇点和可解（幂等）李代数之间建立联系非常重要。在本文中，已构造了一组复杂的解析孤立超曲面奇异点与有限维可解（幂等）李代数之间的新自然联系。我们从孤立的超曲面奇异性自然构造有限维可解（幂等）李代数。这些构造帮助我们从几何角度理解可解（幂等）的李代数。此外，众所周知，高维幂等李代数（$ \ gt 7 $）的分类仍然是一个广阔的领域。在第七维中有一个非参数同构幂等李代数的参数集（但没有两个参数族）。第七维度是此类家庭存在的分水岭。众所周知，不存在小于7个维的族，而很难构造大于7个维的一参数族。在本文中，我们从$ \ tilde {E} _7 $奇异性构造了一个单参数族可维（对幂零）Lie代数，维$ 11 $（对$ 10 $），并证明了弱的Torelli型定理成立。我们还将构造一个单参数族，其维数为$ 12 $（resp。nilpotent）Lie代数。$ \ tilde {E} _8 $奇点表示$ 11 $），并证明Torelli型定理成立。此外，我们研究了新的李代数和丘代数之间的数值关系。最后，还计算了由极少数孤立奇异性引起的新李代数。