Time：15:00-16:00, Thursday, November 28 2024
Venue：E4-233
Speaker：Jackson Ryder, University of New South Wales
Title：Simple Dedekind domains associated to noncommutative projective lines
Abstract：One way of constructing noncommutative projective lines is via a noncommutative analogue of the symmetric algebra for a bimodule of left/right dimension 2 over a pair of fields. These noncommutative projective lines contain a canonical closed subscheme, the (affine open) complement of which we are interested in. We will give a brief introduction to noncommutative projective geometry and the construction of this closed subscheme, before showing that the coordinate ring $\Lambda_{00}$ of the open complement is a noncommutative Dedekind domain. Curiously, these noncommutative Dedekind domains are closely tied to field extensions with dihedral Galois groups, and these dihedral groups determine when $\Lambda_{00}$ is a simple ring.
