Geodesic
A~theorem on two commuting automorphisms, and integrable differential equations
Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 263-279

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Constructions are found for differential equations in an arbitrary continuous associative algebra $\mathfrak A$ that admit an equivalent Lax representation (with spectral parameter) in the space of linear operators acting on $\mathfrak A$. The constructions use commuting automorphisms of $\mathfrak A$. Applications of the main construction are indicated for the construction of integrable Euler equations in the direct sum of the Lie algebras $\operatorname{gl}(n,R)$ and $\operatorname{so}(n,R)$. Constructions are presented for matrix differential equations admitting a Lax representation with several spectral parameters. 
@article{IM2_1991_36_2_a2,
     author = {O. I. Bogoyavlenskii},
     title = {A~theorem on two commuting automorphisms, and integrable differential equations},
     journal = {Izvestiya. Mathematics },
     pages = {263--279},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a2/}
}
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O. I. Bogoyavlenskii. A~theorem on two commuting automorphisms, and integrable differential equations. Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 263-279. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a2/