Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra

Abstract

We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight.

arXiv comment16 pages

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Cited by in corpus (1)

• Rota-Baxter operators on the simple Jordan algebra of matrices of order two