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Abstract: A Jordan algebra J over a field k of characteristic 2 becomes a 2-Lie algebra with Lie product and squaring . We determine the precise ideal structure of in case J is simple finite-dimensional and k is algebraically closed. We also decide which of these algebras have smooth automorphism groups. Finally, we study the derivation algebra of a reduced Albert algebra and show that DerJ has a unique proper nonzero ideal , isomorphic to , with quotient independent of . On the group level, this gives rise to a special isogeny between the automorphism group of J and that of the split Albert algebra, whose kernel is the infinitesimal group determined by . [Copyright &y& Elsevier]

We present in this paper a computational approach to the study of the simplicity of the derivation Lie algebra of the quadratic Jordan algebra H3(Os,−), denoted by f4(Os,−), when the characteristic of the base field is two. We will show not only a collection of routines designed to find identities and construct principal ideals but also a philosophy of how to proceed studying the simplicity of a Lie algebra. We have first implemented the quadratic Jordan structure of H3(Os,−) into the computer system Mathematica (Computing the derivation Lie algebra of the quadratic Jordon Algebra H3(Os,−) at any characteristic, preprint, 2001) and then determined the generic expression of an element of the Lie algebra f4(Os,−)=Der(H3(Os,−)) (see (41)). Once the structure of f4(Os,−) is completely described, it is time to analyze the simplicity by using the strategy mentioned. If the characteristic of the base field is not two, the Lie algebra is simple, but if the characteristic is two, the Lie algebra is not simple and there exists only one proper nonzero ideal I which is 26 dimensional and simple as a Lie algebra. In order to prove this last affirmation, we have used again the set of routines to show the simplicity of the ideal and that it is isomorphic to f4/I, which is also a simple Lie algebra. This isomorphism is constructed from a computed Cartan decomposition of both Lie algebras. [Copyright &y& Elsevier]