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Descripción
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| The talk aims to explain a relation between certain partial differential equations and a particular class of commutative nonassociative algebras. Orthogonal equivalence classes of harmonic cubic homogeneous polynomials solving |Hess P(x)^2=?|x|^2 are in bijection with isomorphism classes of commutative nonassociative algebras for which the traces of multiplication operators vanish and the Killing type form given by tracing the product of multiplication operators is a nondegenerate and invariant bilinear form. There is a surprising range of interesting examples with apparently diverse origins in differential geometry (isoparametric polynomials, Jordan algebras, affine spheres), combinatorics (Steiner triple systems, equiangular tight frames), representation theory (algebras of curvature tensors), and finite group theory and vertex operator algebras (permutation modules, Griess algebras). The talk will describe some of these examples explicitly and indicate some of their common features which appear to make them amenable to classification. | |
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Internacional
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Si |
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ISSN o ISBN
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0000000000000 |
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Entidad relacionada
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Universidad de Linköping, Suecia |
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Nacionalidad Entidad
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SUECIA |
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Lugar del congreso
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Linköping |