Geodesic
On algebras of three-dimensional quaternionic harmonic fields
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 14-28

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A quaternionic field is a pair $p=\{\alpha,u\}$ of function $\alpha$ and vector field $u$ given on a 3d Riemannian maifold $\Omega$ with the boundary. The field is said to be harmonic if $\nabla\alpha=\operatorname{rot}u$ in $\Omega$. The linear space of harmonic fields is not an algebra w.r.t. quaternion multiplication. However, it may contain the commutative algebras, what is the subject of the paper. Possible application of these algebras to the impedance tomography problem is touched on. 
@article{ZNSL_2016_451_a1,
     author = {M. I. Belishev},
     title = {On algebras of three-dimensional quaternionic harmonic fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {14--28},
     publisher = {mathdoc},
     volume = {451},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a1/}
}
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M. I. Belishev. On algebras of three-dimensional quaternionic harmonic fields. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 46, Tome 451 (2016), pp. 14-28. http://geodesic.mathdoc.fr/item/ZNSL_2016_451_a1/