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

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References

SHOWING 1-10 OF 41 REFERENCES

On classification and construction of algebraic Frobenius manifolds

REMARKS ON BIHAMILTONIAN GEOMETRY AND CLASSICAL W-ALGEBRAS

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.

TRANSVERSE POISSON STRUCTURES TO ADJOINT ORBITS IN SEMISIMPLE LIE ALGEBRAS

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