Coloquio de Profesores

23 de octubre de 2024. 11:30 hrs. Salón 131. Departamento de Matemáticas, Cinvestav-IPN

Unirse a Zoom
ID de la reunión: 842 4226 8326
Contraseña: 555964

Dr. Kee Yuen Lam
University of British Columbia, Vancouver, Canada

New methods for constructing non-singular bilinear maps

Resumen: Let $f: R^r \times R^s \longrightarrow R^n$ be a bilinear map. By writing $u \times v$ for $f(u,v)$, one thinks of $f$ as specifying a "generalised vector product'' with right as well as left distributive law, which multiplies an $r$-dimensional vector to an $s$-dimensional one, to result in an $n$-dimensional vector. Examples include the well-known cross product of two vectors of $R^3$ into a third. Another example is the "tensor product" of the same two vectors into $R^9 (= R^3 \otimes R^3)$. The first product has zero divisors; the second doesn't.

To determine (and classify) all generalized vector products without zero divisors has been a long standing open problem. It is quite likely that the most interesting cases of such products are yet to be discovered. In this talk I shall, after a historical survey, present some newly found examples based on the notion of "modified polynomial multiplication". I shall then conclude with some conjectures, with emphasis on their relevance to geometry, topology and data science.