On Algebras of Three-Dimensional Quaternion Harmonic Fields

A quaternion field is a pair p = {α, u} of a function α and a vector field u given on a 3d Riemannian manifold Ω with boundary. A field is said to be harmonic if ∇α = rot u in Ω. The linear space of harmonic fields is not an algebra with respect to quaternion multiplication. However, it may contain commutative algebras, which is the subject of the paper. Possible applications of these algebras to the impedance tomography problem are touched upon. © 2017, Springer Science+Business Media, LLC.