51 research outputs found
Approximation by Müntz spaces on positive intervals
International audienceThe so-called Bernstein operators were introduced by S.N. Bernstein in 1912 to give a constructive proof of Weierstrass' theorem. We show how to extend his result to Müntz spaces on positive intervals
On F-theory Quiver Models and Kac-Moody Algebras
We discuss quiver gauge models with bi-fundamental and fundamental matter
obtained from F-theory compactified on ALE spaces over a four dimensional base
space. We focus on the base geometry which consists of intersecting F0=CP1xCP1
Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds
of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and
indefinite, in particular hyperbolic. We interpret the equations defining these
three classes of generalized Lie algebras as the anomaly cancelation condition
of the corresponding N =1 F-theory quivers in four dimensions. We analyze in
some detail hyperbolic geometries obtained from the affine A base geometry by
adding a node, and we find that it can be used to incorporate fundamental
fields to a product of SU-type gauge groups and fields.Comment: 13 pages; new equations added in section 3, one reference added and
typos correcte
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