Lie bialgebras, fields of cohomological dimension at most 2 and Hilbert's Seventeenth Problem
Artikel i vetenskaplig tidskrift, 2017

We investigate Lie bialgebra structures on simple Lie algebras of non-split type A. It turns out that there are several classes of such Lie bialgebra structures, and it is possible to classify some of them. The classification is obtained using Belavin–Drinfeld cohomology sets, which are introduced in the paper. Our description is particularly detailed over fields of cohomological dimension at most two, and is related to quaternion algebras and the Brauer group. We then extend the results to certain rational function fields over real closed fields via Pfister's theory of quadratic forms and his solution to Hilbert's Seventeenth Problem.

Belavin-Drinfeld cohomology

Lie bialgebra

Quaternions

Compact type

Pfister form

Brauer group

Quantum group

Författare

Seydon Alsaody

Chalmers University of Technology

Alexander Stolin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Journal of Algebra

0021-8693 (ISSN) 1090-266X (eISSN)

Vol. 478 368-394

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1016/j.jalgebra.2016.12.018