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arXiv · 1305.1391

A polynomial identity for the bilinear operation in Lie-Yamaguti algebras

Murray R. Bremner
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Abstract

We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie-Yamaguti algebra. This identity is a consequence of the defining identities for Lie-Yamaguti algebras, but is not a consequence of anticommutativity. We give an explicit form of this identity as an alternating sum over all permutations of the variables in a polynomial with 8 terms. Our computations also show that such identities do not exist in degrees less than 8.

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Murray R. Bremner. 2013-05-07. A polynomial identity for the bilinear operation in Lie-Yamaguti algebras. https://arxiv.org/abs/1305.1391

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