NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


Ernst Dieterich

(University of Uppsala) 

 
Real Division Algebras


ABSTRACT: The problem of classifying all finite-dimensional real division algebras originated in the discovery of the quaternion algebra H (Hamilton, 1843) and the octonion algebra O (Graves, 1843; Cayley, 1845). Frobenius proved (1878) that (R, C, H) classifies all associative real division algebras. Zorn (1931) generalized Frobenius' theorem, proving that (R, C, H, O) classifies all alternative real division algebras. According to theorems of Hopf (1940) and Bott - Milnor (1958), real division algebras exist only in the dimensions 1, 2, 4, 8. The talk will report on this historical development, emphasize the connection between real division algebras and vector fields on spheres, and finally present new results regarding the classification problem of real division algebras.

Date: December 2, 2002
(Notice unusual day)
Time: 10:30 - 11:30
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>