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0111 · Dec 201419922001200920172026
2 results for “Adler-Gelfand-Dickey”
From Adler-Gelfand-Dickey Brackets to Logarithmic Dubrovin-Frobenius manifoldsmath.DG

New Poisson bracket connects to logarithmic manifolds.

problem Constructing a new Poisson bracket compatible with existing structures.
method Developed a new local Poisson bracket compatible with Adler-Gelfand-Dickey brackets, leading to a dispersionless limit.
result Leading term defines a logarithmic Dubrovin-Frobenius manifold.
Poisson bracketDubrovin-Frobenius manifoldAdler-Gelfand-DickeyLogarithmicPermutation group
2025-06-13abs ↗pdf ↗
Swapping algebra, Virasoro algebra and discrete integrable systemmath.DG

We induce a Poisson algebra {⋅,⋅}Cn,N\{\cdot,\cdot\}_{\mathcal{C}_{n,N}} on the configuration space Cn,N\mathcal{C}_{n,N} of NN twisted polygons in RPn−1\mathbb{RP}^{n-1} from the swapping algebra \cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov algebra for n=2n=2. There is another Poisson algebra $\{\cdot,\cdot\}…

2014-12-14abs ↗pdf ↗