On powerful and p-central restricted Lie algebras

Restricted Lie Algebras

REPRESENTATIONS OF RESTRICTED LIE ALGEBRAS OF CHARACTERISTIC p

It was proved by Jacobson [2] that every finite-dimensional Lie algebra of characteristic p has a finite-dimensional representation space which is not semisimple. In this note we prove a similar result for Jacobson's restricted Lie algebras [l]. The structure of a restricted Lie algebra L over a field F of characteristic p comprises, in addition to the ordinary Lie algebra structure, a map x—*-...

Cohomology of Restricted Lie Algebras

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. Motivations for the definition of a restricted Lie algebra are given and the theory of ordinary Lie algebra cohomology is briefly reviewed, including a discussion on algebraic interpretations of the low dimensional cohomology spaces of ordinary Lie algebras. The general Cartan-Eilenberg construction of the st...

Lie $^*$-double derivations on Lie $C^*$-algebras

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

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.