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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.07958 |
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| _version_ | 1866916837404442624 |
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| author | Panyushev, Dmitri Yakimova, Oksana |
| author_facet | Panyushev, Dmitri Yakimova, Oksana |
| contents | Let q be a finite-dimensional Lie algebra and $θ$ an automorphism of q of order m. We extend $θ$ to an automorphism of the loop algebra of q and consider the fixed-point subalgebra $q[t,t^{-1}]^θ$. Using a splitting of $q[t,t^{-1}]^θ$, we construct $θ$-twisted Poisson-commutative versions of the Feigin--Frenkel centre and the universal Gaudin subalgebra introduced by Ilin and Rybnikov in 2021. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants of twisted current algebras and related Poisson-commutative subalgebras Panyushev, Dmitri Yakimova, Oksana Representation Theory Mathematical Physics Let q be a finite-dimensional Lie algebra and $θ$ an automorphism of q of order m. We extend $θ$ to an automorphism of the loop algebra of q and consider the fixed-point subalgebra $q[t,t^{-1}]^θ$. Using a splitting of $q[t,t^{-1}]^θ$, we construct $θ$-twisted Poisson-commutative versions of the Feigin--Frenkel centre and the universal Gaudin subalgebra introduced by Ilin and Rybnikov in 2021. |
| title | Invariants of twisted current algebras and related Poisson-commutative subalgebras |
| topic | Representation Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.07958 |