# Frobenius manifolds from regular classical W-algebras

@article{Dinar2011FrobeniusMF,
title={Frobenius manifolds from regular classical W-algebras},
author={Yassir Dinar},
year={2011},
volume={226},
pages={5018-5040}
}
• Yassir Dinar
• Published 5 January 2010
• Mathematics
14 Citations

### Weights of Semiregular Nilpotents in Simple Lie Algebras of D Type

We compute the weights of the adjoint action of semiregular $sl_2$-triples in simple Lie algebras of type $D_n$ using mathematical induction.

### Conjugate Frobenius Manifold and Inversion Symmetry

• Mathematics
Mathematical 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

### Classical $W$-algebras and Frobenius manifolds related to Liouville completely integrable systems

We proved that the local bihamiltonian structure obtained by generalized Drinfeld-Sokolov reduction associated to a nilpotent element of semisimple type is reduced by Dirac reduction to the loop

### Algebraic classical W-algebras and Frobenius manifolds

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

### Local matrix generalizations of $W$-algebras

In this paper, we propose local matrix generalizations of the classical $W$-algebras based on the second Hamiltonian structure of the $\mathcal{Z}_m$-valued KP hierarchy, where $\mathcal{Z}_m$ is a

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

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

### Ju n 20 21 Inversion symmetry on Frobenius manifolds June 16 , 2021

• Mathematics
• 2021
We give an interpretation of the inversion symmetry of WDVV equations using theory of flat pencil of metrics associated to Frobenius manifolds. Mathematics Subject Classification (2020) 53D45

### Fe b 20 22 Conjugate Frobenius manifold and inversion symmetry February 22 , 2022

• Mathematics
• 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

### The Quadratic WDVV Solution E8(A1)

We calculate explicitly the quadratic solution to the WDVV equations corresponds to the quasi-Coxeter conjugacy class $E_8(a_1)$ using the associated classical $W$-algebra.

## References

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