nLab Milnor algebra

Idea

Milnor algebra $M(f)$ of an analytic function $f$ has a role of describing a germ of singularity of a function modulo the ideal generated by all partial derivatives of the functions.

Literature

Related notions: Tjurina algebra?, singularity, hypersurface singularity?, Jacobian algebra

• Stephen ST Yau, Milnor algebras and equivalence relations among holomorphic functions Bull. Amer. Math. Soc. 9 (1983) 235-239 doi
• wikipedia: Milnor number

There is also a related “Lie algebra of a singularity”(introduced by S S T Yau). See

• A. Elashvili and G. Khimshiashvi, Algebras of simple hypersurface singularities, Journal of Lie Theory 16 (2006) 621–649 pdf