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Topological Lie Bia...
Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]]
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- Abedin, Raschid (författare)
- Eidgenössische Technische Hochschule Zürich (ETH),Swiss Federal Institute of Technology in Zürich (ETH)
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- Maximov, Stepan (författare)
- Padernborn University, Germany
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- Stolin, Alexander, 1953 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Zelmanov, Efim (författare)
- Southern University of Science and Technology
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(creator_code:org_t)
- 2024
- 2024
- Engelska.
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Ingår i: Communications in Mathematical Physics. - 1432-0916 .- 0010-3616. ; 405:1
- Relaterad länk:
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https://doi.org/10.1...
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Abstract
Ämnesord
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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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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