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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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