A Construction of Deformations to General Algebras

One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative finite-dimensional ${\mathbb{C}}$ -algebra $A$ , find algebras $N$ , which can be deformed to $A$ . We develop a simple method that produces associative and flat deformations to investigate this question. As an application of this method we answer a question of Michael Wemyss about deformations of contraction algebras.