Finite-Dimensional Absolute Valued Algebras.

**Hora de inicio:** 10:00. **Hora de fin:** 11:00.

An absolute valued algebra is a non-zero real algebra with a multiplicative norm. In the finite-dimensional case, such algebras exist only in dimensions 1, 2, 4 and 8. Except in dimension eight, they have been classified up to isomorphism, and the homomorphisms between them have been described. While an isomorphism condition exists for the eight-dimensional case as well, the classification problem is still open, and has proven quite hard.

I will present some results on the structure of the class of eight-dimensional absolute valued algebras. The aim is to subdivide the classification problem systematically, while trying to avoid certain inherent technical difficulties.