Lie bialgebras, fields of cohomological dimension at most 2 and Hilbert's Seventeenth Problem

JOURNAL OF ALGEBRA

卷:476

Article

Alsaody, Seidon^1,2  Stolin, Alexander^1,2 

[1] Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden

[2] Univ Gothenburg, S-41296 Gothenburg, Sweden

关键词: Lie bialgebra;    Compact type;    Quantum group;    Belavin-Drinfeld cohomology;    Pfister form;    Quaternions;    Brauer group;   

DOI  :  10.1016/j.jalgebra.2016.12.018

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free