Frobenius manifolds from regular classical W-algebras

@article{Dinar2011FrobeniusMF,
  title={Frobenius manifolds from regular classical W-algebras},
  author={Yassir Dinar},
  journal={Advances in Mathematics},
  year={2011},
  volume={226},
  pages={5018-5040}
}
  • Yassir Dinar
  • Published 5 January 2010
  • Mathematics
  • Advances in Mathematics
View PDF on arXiv
14 Citations
Background Citations
2
Methods Citations
5

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

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

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

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…

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

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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