The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra

Details The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra

2011-08-21

arxiv.org/abs/1108.4202v1

Mathematics

Rings and Algebras

20 pages

Scientific paper

The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible $\mathfrak{sl}(2,\mathbb{C})$-module V(6) with binary product $[x,y] = \alpha(x \wedge y)$ defined by the $\mathfrak{sl}(2,\mathbb{C})$-module morphism $\alpha\colon \Lambda^2 V(6) \to V(6)$. Combining this with the ternary product $(x,y,z) = \beta(x \wedge y) \cdot z$ defined by the $\mathfrak{sl}(2,\mathbb{C})$-module morphism $\beta\colon \Lambda^2 V(6) \to V(2) \approx \s$ gives $M$ the structure of a generalized Lie triple system, or Lie-Yamaguti algebra. We use computer algebra to determine the polynomial identities of low degree satisfied by this binary-ternary structure.

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