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Irreducible binary $$(-1,1)$$-bimodules over simple finite-dimensional algebras. (Russian, English) Zbl 1150.17025
Sib. Mat. Zh. 47, No. 5, 1139-1146 (2006); translation in Sib. Math. J. 47, No. 5, 934-939 (2006).
Summary: We prove that an irreducible binary $$(-1, 1)$$-bimodule over an algebra $$A$$ is alternative in the following cases: (a) $$A$$ is a composition algebra over a field of characteristic different from 2 and 3; (b) $$A$$ is a simple finite-dimensional alternative algebra over a field of characteristic 0.

##### MSC:
 17D20 $$(\gamma, \delta)$$-rings, including $$(1,-1)$$-rings 17D05 Alternative rings 16D20 Bimodules in associative algebras 17A75 Composition algebras 17C20 Simple, semisimple Jordan algebras
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