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>