Degenerations and contractions of algebras and forms

Abstract

This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on the spaces of these two objects. The base field is taken to be infinite of characteristic not 2. It is unrestricted otherwise, as in the first cited paper of Ivanova and Pallikaros. We apply the results to algebras and forms in dimensions two and three.