On (k,l)-th singular locus moduli algebras of singularities and their derivation Lie algebras

Abstract

In this paper, we introduce a series of new invariants to singularities. A new conjecture about the non-existence of negative weight derivations of these new $(k,l)$-th singular locus moduli algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture in some cases.