• 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 $gl(m,\mathbb{C})$.
We introduce Frobenius algebra ℱ-valued (n, m)th KdV hierarchy and construct its bi-Hamiltonian structures by employing ℱ-valued pseudo-differential operators. As an illustrative example, the (1,
• Mathematics
• 2014
We construct the extended flow equations of a new ZN-Toda hierarchy taking values in a commutative subalgebra ZN of gl(N,C). We give the Hirota bilinear equations and tau function of this new
• Mathematics
• 2014
The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a
In this paper, we defined a new multi-component B type Kadomtsev-Petviashvili (BKP) hierarchy that takes values in a commutative subalgebra of gl ( N , C ) . ?> After this, we give the gauge
• Mathematics
• 2015
We introduce a Frobenius algebra-valued Kadomtsev-Petviashvili (KP) hierarchy and show the existence of Frobenius algebra-valued τ-function for this hierarchy. In addition, we construct its
• Mathematics, Physics
• 2020
By taking values in a commutative subalgebra , we construct a new generalized - Heisenberg ferromagnet model in (1+1)-dimensions. The corresponding geometrical equivalence between the generalized -
• Mathematics
• 2012
A bstractWe study conical defect geometries in the SL(N,$\mathbb{R}$) × SL(N,$\mathbb{R}$) (and SL(N,$\mathbb{C}$)) Chern-Simons formulation of higher spin gauge theories in AdS3. We argue that
• Mathematics
Theoretical and Mathematical Physics
• 2015
We construct the extended flow equations of a new ZN-Toda hierarchy taking values in a commutative subalgebra ZN of gl(N,C). We give the Hirota bilinear equations and tau function of this new

## References

SHOWING 1-10 OF 48 REFERENCES

• Mathematics
• 1996
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 +
• Mathematics
Compositio Mathematica
• 2013
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
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
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
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
• Mathematics
• 1989
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