Let (V,0) be an isolated hypersurface singularity defined by the holomorphic function \(f: (\mathbb {C}^{n}, 0)\rightarrow (\mathbb {C}, 0)\). The k-th Yau algebra L^k(V ) is defined to be the Lie algebra of derivations of the k-th moduli algebra \(A^{k}(V) := \mathcal {O}_{n}/(f, m^{k}J(f))\), where k ≥ 0, m is the maximal ideal of \(\mathcal {O}_{n}\). I.e., L^k(V ) := Der(A^k(V ),A^k(V )). These new series of derivation Lie algebras are quite subtle invariants since they capture enough information about the complexity of singularities. In this paper we formulate a conjecture for the complete characterization of ADE singularities by using generalized Cartan matrix C^k(V ) associated to k-th Yau algebras L^k(V ), k ≥ 1. In this paper, we provide evidence for the conjecture and give a new complete characterization for ADE singularities. Furthermore, we compute their other various invariants that arising from the 1-st Yau algebra L¹(V ).

令（V，0）是由全纯函数\（f：（\ mathbb {C} ^ {n}，0）\ rightarrow（\ mathbb {C}，0）\）定义的孤立的超曲面奇点。第k个Yau代数L ^k（V）被定义为第k个模数代数\（A ^ {k}（V）：= \ mathcal {O} _ {n} /（ F，M ^ {K}Ĵ（F））\） ，其中ķ ≥0，米是的最大理想\（\ mathcal {ö} _ {N} \） 。即，L ^k（V）：= Der（A ^k（V），A ^k（V））。这些新的导出Lie代数系列是非常微妙的不变量，因为它们捕获了有关奇点复杂性的足够信息。在本文中，我们通过使用广义的Cartan矩阵制定ADE奇点的完整表征猜想Ç ^ķ（V相关联于）ķ第攸代数大号^ķ（V），ķ ≥1。在本文中，我们为提供证据猜想并给出ADE奇异点的新完整表征。此外，我们计算它们的其他各种不变量，这些不变量是由第1个Yau代数L ¹（V）引起的。