On the Computation of the Codimension of Map Germs Using the Lie Algebra Associated with a Restricted Left–Right Group

Abstract

The codimension is an important invariant, which measures the complexity of map germs and play an important role in classification and recognition problems. The restricted A-equivalence was introduced to obtain a classification of reducible curves. The aim was to classify simple parameterized curves with two components, one of them being smooth with respect to the A-equivalence in characteristic p. In characteristic 0, the corresponding classification was given by Kolgushkin and Sadykov. The aim of this article is to present an algorithm to compute the codimension of germs of singularities under a restricted left–right equivalence (A-symmetry). We also give the implementation of this algorithm in the computer algebra system singular.

On the Conjecture over Dimensions of Associated Lie Algebra to the Isolated Singularities

“…, where L(V) is defined as Der(A(V), A(V)) and V denotes the isolated hypersurface singularity. Lie algebra L(V) is a famous solvable finite-dimensional algebra [5][6][7][8][9][10]. Yau's algebra of V is used in singularity theory to distinguish L(V) from the other types of Lie algebra [11,12].…”