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- Abedin, RaschidPadernborn University, Germany (author)
Classification of classical twists of the standard Lie bialgebra structure on a loop algebra
- Article/chapterEnglish2021
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- Elsevier BV,2021
- electronicrdacarrier
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- LIBRIS-ID:oai:research.chalmers.se:925aacd3-631b-4a78-a01c-81bc81c554b6
- https://research.chalmers.se/publication/523290URI
- https://doi.org/10.1016/j.geomphys.2021.104149DOI
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- Language:English
- Summary in:English
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Classification
Notes
- The standard Lie bialgebra structure on an affine Kac–Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. In this paper we classify all classical twists of the induced Lie bialgebra structures in terms of Belavin–Drinfeld quadruples up to a natural notion of equivalence. To obtain this classification we first show that the induced bialgebra structures are defined by certain solutions of the classical Yang–Baxter equation (CYBE) with two parameters. Then, using the algebro–geometric theory of CYBE, based on torsion free coherent sheaves, we reduce the problem to the well-known classification of trigonometric solutions given by Belavin and Drinfeld. The classification of twists in the case of parabolic subalgebras allows us to answer recently posed open questions regarding the so-called quasi-trigonometric solutions of CYBE.
Subject headings and genre
- NATURVETENSKAP Matematik Algebra och logik hsv//swe
- NATURAL SCIENCES Mathematics Algebra and Logic hsv//eng
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- NATURVETENSKAP Matematik Matematisk analys hsv//swe
- NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
- Loop algebra
- Kac–Moody algebra
- Classical Yang–Baxter equation
- Manin triple
- Trigonometric r-matrices
- Lie bialgebra
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- Maximov, Stepan,1994Chalmers tekniska högskola,Chalmers University of Technology,Göteborgs universitet,University of Gothenburg(Swepub:cth)maximov (author)
- Padernborn University, GermanyChalmers tekniska högskola (creator_code:org_t)
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- In:Journal of Geometry and Physics: Elsevier BV1640393-0440
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