Primary currents and Riemannian geometry in   algebras

Bandelloni, G.; Lazzarini, Serge

doi:10.1016/s0550-3213(01)00252-8

Cited by 2 publications

(4 citation statements)

References 77 publications

(72 reference statements)

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“…which are exactly those coefficients obtained for the so-called W 3 -algebra [14,27]. The last expression is given in terms of the projective connection and the structure functions only.…”

Section: The Forsyth Framessupporting

confidence: 62%

“…The present upshot greatly improves some previous work [27,31] in the sense that it is now possible to construct explicitly the X -term which breaks by truncation the W ∞ -symmetry governed by an underlying symplectomorphism symmetry [11,32] to a finite W s -algebra.…”

Section: Covariance Under Holomorphic Reparametrizationsupporting

confidence: 51%

“…Next, we get the well known transformations [12,27] upon redefining C (2) = 1 2 C (2) by a numerical rescaling…”

Section: The W 3 Examplementioning

confidence: 99%

“…(3) (z, z|3) K (2) (z, z|3) = C (2) (z, z), (6.22) and depends only on the level s = 3. Next, we get the well known transformations [12,27] upon redefining 2) by a numerical rescaling 2) (z, z)∂C (2) (z, z)…”

Section: The W 3 Examplementioning

confidence: 99%

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Large chiral diffeomorphisms on Riemann surfaces and W-algebras

Bandelloni

Lazzarini

2006

Journal of Mathematical Physics

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The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphims.

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“…which are exactly those coefficients obtained for the so-called W 3 -algebra [14,27]. The last expression is given in terms of the projective connection and the structure functions only.…”

Section: The Forsyth Framessupporting

confidence: 62%