Geodesic
Constants of partial derivations and primitive operations
Algebra i logika, Tome 56 (2017) no. 3, pp. 317-347

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We describe algebras of constants of the set of all partial derivations in free algebras of unitarily closed varieties over a field of characteristic 0. These constants are also called eigenpolynomials. It is proved that a subalgebra of eigenpolynomials coincides with the subalgebra generated by values of commutators and Umirbaev–Shestakov primitive elements $p_{m,n}$ on a set of generators for a free algebra. The space of primitive elements is a linear algebraic system over a signature $\Sigma=\{[x,y],p_{m,n}\mid m,n\ge1\}$. We point out bases of operations of the set $\Sigma$ in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.
Keywords: primitive operations, eigenpolynomials, free algebras. 
@article{AL_2017_56_3_a2,
     author = {S. V. Pchelintsev and I. P. Shestakov},
     title = {Constants of partial derivations and primitive operations},
     journal = {Algebra i logika},
     pages = {317--347},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_3_a2/}
}
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S. V. Pchelintsev; I. P. Shestakov. Constants of partial derivations and primitive operations. Algebra i logika, Tome 56 (2017) no. 3, pp. 317-347. http://geodesic.mathdoc.fr/item/AL_2017_56_3_a2/