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Topological Manin pairs and (n, s)-type series
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- Abedin, R. (författare)
- Eidgenössische Technische Hochschule Zürich (ETH),Swiss Federal Institute of Technology in Zürich (ETH)
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- Maximov, S. (författare)
- Padernborn University, Germany
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- Stolin, Alexander, 1953 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2023
- Engelska.
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Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 113:3
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Abstract
Ämnesord
Stäng
- Lie subalgebras of L = g((x)) x g[x]/x(n)g[x], complementary to the diagonal embedding Delta of g[x] and Lagrangian with respect to some particular form, are in bijection with formal classical r-matrices and topological Lie bialgebra structures on the Lie algebra of formal power series g[x]. In this work we consider arbitrary subspaces of L complementary to Delta and associate them with so-called series of type (n, s). We prove that Lagrangian subspaces are in bijection with skew-symmetric (n, s)-type series and topological quasi-Lie bialgebra structures on g[x]. Using the classificaiton of Manin pairs we classify up to twisting and coordinate transformations all quasi-Lie bialgebra structures. Series of type (n, s), solving the generalized classical Yang-Baxter equation, correspond to subalgebras of L. We discuss their possible utility in the theory of integrable systems.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
Nyckelord
- Lie bialgebras
- quasi-Lie bialgebras
- Manin pairs
- Yang-Baxter
- equations
- r-matrices
- Lie algebra splittings
- Physics
- Lie algebra splittings
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)