Classification of commutative algebras and tube realizations of hyperquadrics

Abstract

In this paper we classify up to affine equivalence all local tube realizations of real hyperquadrics in C^n. We show that this problem can be reduced to the classification, up to isomorphism, of commutative nilpotent real and complex algebras. We also develop some structure theory for commutative nilpotent algebras over arbitrary fields of characteristic zero.

24 pages

Cited by in corpus (5)

• Local tube realizations of CR-manifolds and maximal abelian subalgebras
• Nilpotent algebras and affinely homogeneous surfaces
• On the Affine Homogeneity of Algebraic Hypersurfaces Arising from Gorenstein Algebras
• Isolated hypersurface singularities and polynomial realizations of affine quadrics
• Extracting Invariants of Isolated Hypersurface Singularities from their Moduli Algebras