Automorphism Group of k (( t )):¶Applications to the Bosonic String

Porras, J. M. Muñoz; Martı́n, Francisco

doi:10.1007/s002200000358

Cited by 12 publications

(14 citation statements)

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“…To see that the action of SGl C((z)) (V ) is locally transitive, it suffices to prove that the orbit morphism is surjective at the level of tangent spaces [8]. That is, we have to check that…”

Section: Proposition 34 We Have a Canonical Exact Sequence Of Groupmentioning

confidence: 98%

“…Following previous ideas [8], the definition of this group functor for points with values in any C-scheme can be given.…”

Section: Definition 33mentioning

confidence: 99%

“…Arbarello et al explicitly showed a connection between the representation theory of the Virasoro algebra and the moduli space of line bundles over pointed curves (with formal extra data) [7]. The infinitesimal version of Mumford's formula is another example of this fruitful approach [8].…”

Section: Introductionmentioning

confidence: 98%

“…This should be thought of as a higher rank generalization of the infinitesimal version of the Mumford formula [8].…”

Section: Introductionmentioning

confidence: 99%

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Geometric approach to Kac–Moody and Virasoro algebras

González

Serrano

Porras

et al. 2012

Journal of Geometry and Physics

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a b s t r a c tIn this paper we show the existence of a group acting infinitesimally transitively on the moduli space of pointed-curves and vector bundles (with formal trivialization data) and whose Lie algebra is an algebra of differential operators. The central extension of this Lie algebra induced by the determinant bundle on the Sato Grassmannian is precisely a semidirect product of a Kac-Moody algebra and the Virasoro algebra. As an application of this geometric approach, we give a local Mumford-type formula in terms of the cocycle associated with this central extension. Finally, using the original Mumford formula we show that this local formula is an infinitesimal version of a general relation in the Picard group of the moduli of vector bundles on a family of curves (without any formal trivialization).

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Section: Proposition 34 We Have a Canonical Exact Sequence Of Groupmentioning

confidence: 98%

“…Following previous ideas [8], the definition of this group functor for points with values in any C-scheme can be given.…”

Section: Definition 33mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

“…This should be thought of as a higher rank generalization of the infinitesimal version of the Mumford formula [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Geometric approach to Kac–Moody and Virasoro algebras

González

Serrano

Porras

et al. 2012

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

“…Further, since V is the C((z))-algebra C((z)) × · · · × C((z)), the group G := Aut(C((z))) (see [18] for its definition and properties) acts on Gr(C((z))) and on Gr(V ). If G + is the subgroup of G representing "coordinate changes" of the curve downstairs ( [18]), then Φ is a G + -principal bundle, that is, H(g, 0; 1, .…”

Section: Remark 53mentioning

confidence: 99%