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

Abstract

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 Lkl(V) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra Mnl(V):=Ol/⟨F,Jn⟩, i.e., Lkl(V)=Der(Mnl(V)). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras Lkl(V) under certain condition and prove it true for Lkl(V) when k,l=2.

Keywords

• higher Nash blow-up
• Jacobian matrix
• Cartan matrix
• isolated singularity