Higher dimensional classicalW-algebras

Martínez-Morás, Fernando; Ramos, Eduardo

doi:10.1007/bf02096883

Cited by 8 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The brackets induced on the w j (u i ) by the above mapping coincide with those computed with J cl L p , up to a global factor p 2 [12]. It is worth noting that even for the higher dimensional generalization of the classical Gelfand-Dickey brackets that were constructed in [13] the two previous theorems hold. This is not at all obvious since, for example, this construction uses not one but two different splittings.…”

mentioning

confidence: 58%

The constrained KP hierarchy and the generalised Miura transformation

Mas

Ramos

1995

Physics Letters B

Self Cite

View full text Add to dashboard Cite

Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L = AB −1 . Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem. ♯

show abstract

mentioning

confidence: 58%

The constrained KP hierarchy and the generalised Miura transformation

Mas

Ramos

1995

Physics Letters B

Self Cite

View full text Add to dashboard Cite

show abstract

“…which are defined in a similar way to tensor operators (26), but replacing the angular momentum operatorsĴ (N ) by the coordinates x = (cos ϕ sin ϑ, sin ϕ sin ϑ, cos ϑ), i.e. its covariant symbols (20). Indeed, the large-N structure constants can be calculated through the scalar product (see [28]):…”

Section: Tensor Operator Algebras Of Su(2) and Large-n Matrix Modelsmentioning

confidence: 99%

“…Also, W ∞ (2, 2) was interpreted as a higher-conformal-spin extension of the diffeomorphism algebra diff(4) of vector fields on a 4-dimensional manifold (just as W ∞ is a higher-spin extension of the Virasoro diff(1) algebra), thus constituting a potential gauge guide principle towards the formulation of of induced conformal gravities (Wess-Zumino-Witten-like models) in realistic dimensions [18]. For completeness, let as say that W ∞ -algebras also appear as central extensions of the algebra of (pseudo-)differential operators on the circle [19], and higher-dimensional analogues have been constructed in that context [20]; however, we do not find a clear connection with our construction.…”

Section: Introductionmentioning

confidence: 99%

Generalized higher-spin algebras and symbolic calculus on flag manifolds

Calixto¹

2006

Journal of Geometry and Physics

View full text Add to dashboard Cite

We study a new class of infinite-dimensional Lie algebras W ∞ (N + , N − ) generalizing the standard W ∞ algebra, viewed as a tensor operator algebra of SU (1, 1) in a grouptheoretic framework. Here we interpret W ∞ (N + , N − ) either as an infinite continuation of the pseudo-unitary symmetry U (N + , N − ), or as a "higher-U (N + , N − )-spin extension" of the diffeomorphism algebra diff(N + , N − ) of the N = N + + N − torus U (1) N . We highlight this higher-spin structure of W ∞ (N + , N − ) by developing the representation theory of U (N + , N − ) (discrete series), calculating higher-spin representations, coherent states and deriving Kähler structures on flag manifolds. They are essential ingredients to define operator symbols and to infer a geometric pathway between these generalized W ∞ symmetries and algebras of symbols of U (N + , N − )-tensor operators. Classical limits (Poisson brackets on flag manifolds) and quantum (Moyal) deformations are also discussed. As potential applications, we comment on the formulation of diffeomorphism-invariant gauge field theories, like gauge theories of higher-extended objects, and non-linear sigma models on flag manifolds.

show abstract

“…The three-dimensional generalization 2u tx + (uu x ) x − u yy − u zz = 0 (1.3) and its symmetries were studied by Krasil'shchik, Lychagin and Vinogradov [17] (1986) and by Schwarz [25] (1987). Martinez-Moras and Ramos [18] (1993) showed that the higher dimensional classical W-algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy. Kacdryavtsev and Sapozknikov [9] (1998) found the symmetries for a generalized Khokhlov-Zabolotskaya equation.…”

Section: Introductionmentioning

confidence: 99%

Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations

2008

Preprint

View full text Add to dashboard Cite

Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a diffraction sound beam in a nonlinear medium.We give a new algebraic method of solving these equations by using certain finite-dimensional stable range of the nonlinear terms and obtain large families of new explicit exact solutions parameterized by several functions for them. These parameter functions enable one to find the solutions of some related practical models and boundary value problems.

show abstract

Higher dimensional classicalW-algebras

Cited by 8 publications

References 12 publications

The constrained KP hierarchy and the generalised Miura transformation

The constrained KP hierarchy and the generalised Miura transformation

Generalized higher-spin algebras and symbolic calculus on flag manifolds

Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations

Contact Info

Product

Resources

About