38 citations · 123 across the 28 of their papers we have counts for
29 papers
Commutative algebras satisfying univariate identities with vanishing Peirce polynomial
Daniel J. F. Fox, Vladimir G. Tkachev
We introduce and study -palintropic algebras, a class of commutative algebras defined by the identity . This specific relation is the simplest gen…
Sectional nonassociativity of metrized algebras
Daniel J. F. Fox
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 t…
Killing metrized commutative nonassociative algebras associated with Steiner triple systems
Daniel J. F. Fox
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…
Conelike radiant structures
Daniel J. F. Fox
Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulatio…
Curvature equations coupling symmetric tensors with a metric
Daniel J. F. Fox
There are described hierarchies of equations coupling a metric with a trace-free tensor having prescribed symmetries and in the kernel of certain generalized gradients. These speci…
Commutative algebras with nondegenerate invariant trace form and trace-free multiplication endomorphisms
Daniel J. F. Fox
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 m…