Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]]

Abedin, RaschidEidgenössische Technische Hochschule Zürich (ETH),Swiss Federal Institute of Technology in Zürich (ETH) (author)

The main result of the paper is classification of topological Lie bialgebra structures on the Lie algebra g[[x]] , where g is a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0. We introduce the notion of a topological Manin pair (L,g[[x]]) and present their classification by relating them to trace extensions of F[[x]] . Then we recall the classification of topological doubles of Lie bialgebra structures on g[[x]] and view it as a special case of the classification of Manin pairs. The classification of topological doubles states that up to an appropriate equivalence there are only three non-trivial doubles. It is proven that topological Lie bialgebra structures on g[[x]] are in bijection with certain Lagrangian Lie subalgebras of the corresponding doubles. We then attach algebro-geometric data to such Lagrangian subalgebras and, in this way, obtain a classification of all topological Lie bialgebra structures with non-trivial doubles. For F= C the classification becomes explicit. Furthermore, this result enables us to classify formal solutions of the classical Yang–Baxter equation.

Maximov, StepanPadernborn University, Germany (author)
Stolin, Alexander,1953Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences(Swepub:gu)xstoal (author)
Zelmanov, EfimSouthern University of Science and Technology (author)
Padernborn University, GermanyEidgenössische Technische Hochschule Zürich (ETH) (creator_code:org_t)

By the author/editor: Abedin, Raschid; Maximov, Stepan; Stolin, Alexande ...; Zelmanov, Efim

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Algebra and Logi ...

By the university: Chalmers University of Technology; University of Gothenburg

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.