Flexible division algebras

Conferenciante: Prof. Erik Darpö, de la Universidad de Uppsala (Suecia).
Fecha, hora y lugar: 30 de enero de 2008, a las 12 horas, en el Seminario del Departamento de Álgebra y Análisis Matemático.
Abstract: The study of real division algebras originates in the discoveries of the quaternion and octonion algebras in the middle of the nineteenth century. Classical theorems assert that the real numbers, the complex numbers and the quaternions are, up to isomorphism, the only finite-dimensional associative real division algebras (Frobenius 1878), and that every finite-dimensional alternative division algebra is either associative or isomorphic to the octonions (Zorn 1931). Furthermore, every finite-dimensional real division algebra has dimension one, two, four or eight (Bott, Milnor, Kervaire 1958).

In spite of these decisive results, the problem of classifying all finite-dimensional real division algebras is still far from being solved in full generality. However, classifications have been obtained for several important subclasses, such as commutative (Hopf, Burdujan) and power associative (Osborn, Dieterich) real division algebras. In the present talk, we discuss the classification of all flexible finite-dimensional real division algebras, which was completed just recently.