Friday, June 17 | |
Geometry and matrix analysis
Time: 12:30
Speaker: Marina Tvalavadze (University of Toronto Mississauga) Title: "Variety of real division algebras" Room: zoom Abstract: 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 Dn of n-dimensional unital RDAs as a topological space parametrized by structure constants. Then we prove that Dn is an open subset of Un, the set of all unital n-dimensional algebras which implies that any polynomial identity valid in Dn also holds in Un, and vice versa. | |
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