Derivations of a Finite Dimensional Jb∗-triple (after Meyberg)
نویسنده
چکیده
and [[xy]z] + [[yz]x] + [[zx]y] = 0. Left multiplication in a Lie algebra is denoted by ad(x): ad(x)(y) = [x, y]. An associative algebra A becomes a Lie algebra A− under the product, [xy] = xy − yx. The first axiom implies that [xy] = −[yx] and the second (called the Jacobi identity) implies that x 7→ adx is a homomorphism of L into the Lie algebra (EndL)−, that is, ad [xy] = [adx, ad y]. Assuming that L is finite dimensional, the Killing form is defined by λ(x, y) = tr (ad(x)ad(y)).
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