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

Seydon Alsaody ; Alexander Stolin (Institutionen för matematiska vetenskaper, Algebra och geometri)
Journal of Algebra (0021-8693). Vol. 478 (2017), p. 368-394.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Lie bialgebra, Compact type, Quantum group, Belavin-Drinfeld cohomology, Pfister form, Quaternions, Brauer group

Denna post skapades 2017-01-26. Senast ändrad 2017-07-03.
CPL Pubid: 247728


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Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)



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