# Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures

@article{Dubrovin2007FrobeniusMA, title={Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures}, author={Boris Dubrovin and Si‐Qi Liu and You-jin Zhang}, journal={Advances in Mathematics}, year={2007}, volume={219}, pages={780-837} }

## 61 Citations

### REMARKS ON BIHAMILTONIAN GEOMETRY AND CLASSICAL W-ALGEBRAS

- Mathematics
- 2009

We obtain a local bihamiltonian structure for any nilpotent element in a simple Lie algebra from the generalized bihamiltonian reduction. We prove that this structure can be obtained by performing…

### Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro Symmetries

- MathematicsCommunications in Mathematical Physics
- 2022

We prove that for any tau-symmetric bihamiltonian deformation of the tau-cover of the Principal Hierarchy associated with a semisimple Frobenius manifold, the deformed tau-cover admits an infinite…

### A new construction of the Drinfeld–Sokolov hierarchies

- MathematicsPartial Differential Equations in Applied Mathematics
- 2022

### Algebraic classical W-algebras and Frobenius manifolds

- MathematicsLetters in Mathematical Physics
- 2021

We consider Drinfeld–Sokolov bihamiltonian structure associated with a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On…

### Classical r-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics

- Mathematics
- 2015

A general scheme for the construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to Witten–Dijkgraaf–Verlinde–Verlinde associativity equations is…

### Lecture Notes on Bihamiltonian Structures and Their Central Invariants

- Mathematics
- 2018

In these lecture notes, we give an introduction to the classification theorem of semisimple bihamiltonian structures, with as much details as possible. The equivalence classes of this classification…

### $W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

- Mathematics
- 2009

### Conjugate Frobenius Manifold and Inversion Symmetry

- MathematicsMathematical Physics, Analysis and Geometry
- 2022

We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of…

### On the Drinfeld–Sokolov Hierarchies of D Type

- Mathematics
- 2009

We extend the notion of pseudo-differential operators that are used to represent the Gelfand–Dickey hierarchies and obtain a similar representation for the full Drinfeld–Sokolov hierarchies of D n…

### Integrable systems associated to open extensions of type A and D Dubrovin–Frobenius manifolds

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We investigate the solutions to open WDVV equation, associated to type A and D Dubrovin–Frobenius manifolds. We show that these solutions satisfy some stabilization condition and associate to both of…

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