Frobenius manifolds from regular classical W-algebras

  title={Frobenius manifolds from regular classical W-algebras},
  author={Yassir Dinar},
  journal={Advances in Mathematics},
  • Yassir Dinar
  • Published 5 January 2010
  • Mathematics
  • Advances in Mathematics

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

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.



On classification and construction of algebraic Frobenius manifolds


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

Simple Singularities and Simple Algebraic Groups

Regular group actions.- Deformation theory.- The quotient of the adjoint action.- The resolution of the adjoint quotient.- Subregular singularities.- Simple singularities.- Nilpotent elements in

Introduction to Lie Algebras and Representation Theory

Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-

The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group

Let g be a complex simple Lie algebra and let G be the adjoint group of g. It is by now classical that the Poincare polynomial p G (t) of G factors into the form

Drinfeld-Sokolov reduction on a simple lie algebra from the bihamiltonian point of view

We show that the Drinfeld-Sokolov reduction can be framed in the general theory of bihamiltonian manifolds, with the help of a specialized version of a reduction theorem for Poisson manifolds by

Lie algebras and equations of Korteweg-de Vries type

The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and

Geometry of 2D topological field theories

These lecture notes are devoted to the theory of “equations of associativity” describing geometry of moduli spaces of 2D topological field theories.


We study the transverse Poisson structure to adjoint orbits in a complex semisimple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen