Invariants of twisted current algebras and related Poisson-commutative subalgebras

2025/07/10 by Dmitri I. Panyushev, Panyushev, Dmitri, Oksana Yakimova +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.07958

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Some remarks on periodic gradings
• A bi-Hamiltonian nature of the Gaudin algebras
• Periodic automorphisms, compatible Poisson brackets, and Gaudin\n subalgebras
• On classical limits of Bethe subalgebras in Yangians
• Takiff algebras with polynomial rings of symmetric invariants
• One-parameter contractions of Lie-Poisson brackets
• Uniqueness of higher Gaudin hamiltonians

Related

• Periodic automorphisms, compatible Poisson brackets, and Gaudin\n subalgebras
• Extended Symmetries and Poisson Algebras Associated to Twisted Dirac Structures
• Shifts of semi-invariants and complete commutative subalgebras in polynomial Poisson algebras
• Some remarks on periodic gradings
• Bialgebra actions, twists, and universal deformation formulas