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pro vyhledávání: '"Fox, Daniel P."'
Hsiang algebras are a class of nonassociative algebra defined in terms of a relation quartic in elements of the algebra. This class arises naturally in relation to the construction of real algebraic minimal cones. Additionally, Hsiang algebras were c
Externí odkaz:
http://arxiv.org/abs/2410.14267
Autor:
Fox, Daniel J. F.
Publikováno v:
Annali di Matematica Pura ed Applicata, 2023
The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a pseudo-Riemannian metric, with the associator in place of the Levi-Civita covariant derivative. For co
Externí odkaz:
http://arxiv.org/abs/2211.01073
Autor:
Fox, Daniel J. F.
Publikováno v:
Journal of Algebra. Vol. 608, No. 15 (2022), pp. 186-213
With each Steiner triple system there is associated a one-parameter family of commutative, nonassociative, nonunital algebras that are by construction exact, meaning that the trace of every multiplication operator vanishes, and these algebras are sho
Externí odkaz:
http://arxiv.org/abs/2205.08838
Autor:
Fox, Daniel J. F.
Publikováno v:
Information Geometry, Vol. 6, No. 2 (2023) pp.463-595
Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures that genera
Externí odkaz:
http://arxiv.org/abs/2106.04270
Autor:
Fox, Daniel J. F.
There are described equations coupling a completely symmetric conformal Killing or Codazzi tensor to the Einstein equations for a metric, in a manner analogous to that used to obtain the Einstein-Maxwell equations by coupling a two-form to the metric
Externí odkaz:
http://arxiv.org/abs/2105.05514
Autor:
Fox, Daniel J. F.
A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither unital nor as
Externí odkaz:
http://arxiv.org/abs/2004.12343
Autor:
Fox, Daniel J. F.
Publikováno v:
Anal.Math.Phys. 11, 43 (2021)
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutio
Externí odkaz:
http://arxiv.org/abs/1905.00071
Autor:
Fox, Daniel J. F.
Publikováno v:
Forum of Mathematics, Sigma 9 (2021) e79
The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with respect to the symmetric bilinear form determined by the metr
Externí odkaz:
http://arxiv.org/abs/1901.04012
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Autor:
Venugopal Hari, Mobbs Jesse, Taveneau Cyntia, Fox Daniel, Knott Gavin, Grinter Rhys, Thal David, Ramm Georg
Publikováno v:
BIO Web of Conferences, Vol 129, p 11010 (2024)
Externí odkaz:
https://doaj.org/article/57df53c391d14c1cb6002f4488fa72c9
