# Thomas Unger: Extending orderings and valuations to algebras with involution

Date of publication: 4. 2. 2021

Mathematics colloquium

Wednesday

10

February

Time:

14:15 - 15:45

Location:

Zoom

ID: 952 1045 6981
–
Password: 683164

Central simple algebras with involution are a very active area of current research in algebra
with many connections to other parts of mathematics. In the last number of years, Vincent
Astier and myself have been developing the “real theory” of algebras with involution, which
means investigating these objects in the presence of orderings on the base field. A natural
question that arises (and that is motivated by the theory of positive semidefinite matrices
and results on signatures of hermitian forms), is wether orderings can be extended from
the base field to the algebra, and how much of the Artin-Schreier theory of ordered fields
carries over. Another question is to see how much of the Baer-Krull theory (the behaviour
of orderings under real places) carries over. Pretty soon after these results were established
for fields, extensions in the noncommutative direction were attempted, some of which more
successful than others, but none really ticking all the boxes. In my talk I will discuss our
work on “positive cones” and their canonically associated Tignol-Wadsworth gauges in this
context, which so far already has produced several promising results.

Predavanje je izjemoma v **sredo** ob **14:15**. Vljudno vabljeni!

Primož Moravec