• Corpus ID: 117294133

Local matrix generalizations of $W$-algebras

@article{Zuo2014LocalMG,
  title={Local matrix generalizations of \$W\$-algebras},
  author={Dafeng Zuo},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
  • Dafeng Zuo
  • Published 10 January 2014
  • Mathematics
  • arXiv: Mathematical Physics
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 maximal commutative subalgebra of $gl(m,\mathbb{C})$. 
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12 Citations
Highly Influential Citations
1
Background Citations
2
Methods Citations
7

12 Citations

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References

SHOWING 1-10 OF 48 REFERENCES

New integrable hierarchies from vertex operator representations of polynomial Lie algebras

Frobenius manifolds from regular classical W-algebras

Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

AbstractIn analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $$L = p^n +…

$\mathcal {W}$-constraints for the total descendant potential of a simple singularity

Abstract Simple, or Kleinian, singularities are classified by Dynkin diagrams of type $ADE$. Let $\mathfrak {g}$ be the corresponding finite-dimensional Lie algebra, and $W$ its Weyl group. The set…

Higher spin fields and the Gelfand-Dickey algebra

We show that in 2-dimensional field theory, higher spin algebras are contained in the algebra of formal pseudodifferential operators introduced by Gelfand and Dickey to describe integrable nonlinear…

Bihamiltonian structure of the KP hierarchy and the WKP algebra

Lectures on Classical W-Algebras

These are lecture notes of lectures given in 1993 in Cortona, Italy. W-algebras appeared in the conformal field theory as extensions of the Virasoro algebra. They are closely connected with…

Extended Classical Conformal Algebras and the Second Hamiltonian Structure of Lax Equations

Non-local matrix generalizations ofW-algebras

There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinarymth-order linear differential…

Classical r-matrices and compatible Poisson brackets for coupled KdV systems

AbstractThe formalism of classical r-matrices is used to construct families of compatible Poisson brackets for some nonlinear integrable systems connected with Virasoro algebras. We recover the…