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Topological Lie Bia...
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Abedin, RaschidEidgenössische Technische Hochschule Zürich (ETH),Swiss Federal Institute of Technology in Zürich (ETH)
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Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]]
- Article/chapterEnglish2024
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LIBRIS-ID:oai:research.chalmers.se:d4689be6-ce89-4350-8b06-e371a221b8bc
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https://research.chalmers.se/publication/539553URI
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https://doi.org/10.1007/s00220-023-04911-6DOI
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https://gup.ub.gu.se/publication/334878URI
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Language:English
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Summary in:English
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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.
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Maximov, StepanPadernborn University, Germany
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Stolin, Alexander,1953Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences(Swepub:gu)xstoal
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Zelmanov, EfimSouthern University of Science and Technology
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Padernborn University, GermanyEidgenössische Technische Hochschule Zürich (ETH)
(creator_code:org_t)
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In:Communications in Mathematical Physics405:11432-09160010-3616
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