The so-called Lvov-Kaplansky Conjecture states that the image of a multilinear polynomial evaluated on the matrix algebra or order n is always a vector subspace. A solution to this problem is known only for n=2. In this talk we will present analogous conjectures for other associative and non-associative algebras and for graded algebras. Also, we will show how we can use gradings to present a statement equivalent to the Lvov-Kaplansky conjecture.
This video is part of the European Non-Associative Algebra Seminar series.
