22,392 research outputs found
Toroidal vertex algebras and their modules
We develop a theory of toroidal vertex algebras and their modules, and we
give a conceptual construction of toroidal vertex algebras and their modules.
As an application, we associate toroidal vertex algebras and their modules to
toroidal Lie algebras.Comment: 36 page
M\"obius and Laguerre geometry of Dupin Hypersurfaces
In this paper we show that a Dupin hypersurface with constant M\"{o}bius
curvatures is M\"{o}bius equivalent to either an isoparametric hypersurface in
the sphere or a cone over an isoparametric hypersurface in a sphere. We also
show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre
equivalent to a flat Laguerre isoparametric hypersurface. These results solve
the major issues related to the conjectures of Cecil et al on the
classification of Dupin hypersurfaces.Comment: 45 pages. arXiv admin note: text overlap with arXiv:math/0512090 by
other author
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