### Weighted homogeneous polynomials with isomorphic milnor algebras

JPRM-Vol. 1 (2012), Issue 1, pp. 106 – 114 Open Access Full-Text PDF

**Imran Ahmed**

**Abstract:**We recall first some basic facts on weighted homogeneous functions and filtrations in the ring A of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor algebra is a complete invariant for the classification of weighted homogeneous polynomials with respect to right-equivalence, i.e. change of coordinates in the source and target by diffeomorphism.