The derivation algebras of the classical infinite Lie algebras

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

Infinite-dimensional Lie algebras

Classical Lie Algebras

Classical Lie algebras

1 Classical Lie algebras A Lie algebra is a vector space g with a bilinear map [, ] : g× g → g such that (a) [x, y] = −[y, x], for x, y ∈ g, and (b) (Jacobi identity) [x, [y, z]] + [z, [x, y]] + [y, [z, x]] = 0, for all x, y, z ∈ g. A bilinear form 〈, 〉 : g× g → C is ad-invariant if, for all x, y, z ∈ g, 〈adx(y), z〉 = −〈y, adx(z)〉, where adx(y) = [x, y], (1.1) for x, y,∈ g. The Killing form is ...

On Derivation Algebras of Malcev Algebras and Lie Triple Systems

W. H. Davenport has shown that the derivation algebra 3)(4) of a semisimple Malcev algebra A of characteristic 0 acts completely reducibly on A. The purpose of the present note is to characterize those Malcev algebras which have such derivation algebras as those whose radical is central and to obtain the same result for Lie triple systems. Analogous results are known to hold for standard and al...