On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities.

It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras L k l (V) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra M n l (V) : = O l / 〈 F , J n 〉 , i.e., L k l (V) = D e r (M n l (V)) . In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras L k l (V) under certain condition and prove it true for L k l (V) when k , l = 2 . [ABSTRACT FROM AUTHOR]