How to recover an algebra structure if the algebra does NOT satisfy any reasonable identity? How to characterize its idempotents, their spectrum, or fusion laws? In my talk, I will discuss what can be thought of as “non-associative algebra in large”, imitating a well-known concept of “geometry in large”. In other words, the properties of non-associative algebras which crucially depend on a complete set of idempotents. The latter is very related to the concept of generic algebras. I will explain some recent results in this direction and some unsolved problems.
This video is part of the European Non-Associative Algebra Seminar series.
