Geometry and matrix analysis

Speaker: Marina Tvalavadze (University of Toronto Mississauga )

"Variety of real division algebras"

Time: 12:30

Room: zoom

I will start my presentation with a short overview of classical real division algebras (RDAs) such as R (the real numbers), C (the complex numbers), H (the quaternions) and O (the octonions). Then we recall the famous Frobenius theorem and Bott-Milnor-Kervaire theorem about the dimension of a finite-dimensional RDA. Following Kuzmin's paper, we view the set $D_n$ of n-dimensional unital RDAs as a topological space parametrized by structure constants. Then we prove that $D_n$ is an open subset of $U_n$, the set of all unital n-dimensional algebras which implies that any polynomial identity valid in $D_n$ also holds in $U_n$, and vice versa.