Weighted homogeneous polynomials with isomorphic milnor algebras

Imran Ahmed
Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan.

\(^{1}\)Corresponding Author: drimranahmed@ciitlahore.edu.pk.

Copyright © 2012 Imran Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2012.

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.

Keywords:

Milnor algebra, right-equivalence, weighted homogeneous polynomial.