Topological Manin pairs and (n, s)-type series

Abedin, R. (författare): Eidgenössische Technische Hochschule Zürich (ETH),Swiss Federal Institute of Technology in Zürich (ETH)

Stolin, Alexander, 1953 (författare): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology

(creator_code:org_t)

2023
2023
Engelska.
Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 113:3

Relaterad länk:: https://research.cha... (primary) (free); visa fler...; https://gup.ub.gu.se...; https://doi.org/10.1...; https://research.cha...; visa färre...

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.

Om ämnet

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.