Department Mathematik



Yorck Sommerhäuser


Azumaya Algebras and Brauer Groups
(Azumaya-Algebren und Brauergruppen)

  • Summer semester 2002
  • Time: Friday, 11:15 am
  • Room: 251
  • Planning session: Friday, April 19, 2002, 11:15 am, Room 251
  • Contents: While over algebraically closed fields every semisimple algebra is a product of matrix algebras over the base field, over not algebraically closed fields matrix rings over division rings also occur, in the case of the real numbers for example the quaternions. The question which semisimple algebras and which division rings are possible over a given base field leads to interesting connections to other properties of the field, for example to its Galois cohomology groups. In the seminar, we first develop this theory over fields and afterwards consider its generalization for rings. This theory, which is comparatively old for the rings considered in number theory, has recently attacted the attention of the string theorists through its application to rings of differentiable functions.
  • Seminar program (german, dvi)
  • Seminar workout