On Herstein's Lie Map Conjectures, II

Beilinson’s conjectures II

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 ...

On the Moment Map for the Variety of Lie Algebras

We consider the moment map m : PVn 7→ iu(n) for the action of GL(n) on Vn = Λ(C) ⊗ C. The critical points of the functional Fn = ||m|| : PVn 7→ R are studied, in order to understand the stratification of Ln ⊂ PVn defined by the negative gradient flow of Fn, where Ln is the algebraic subset of all Lie algebras. We obtain a description of the critical points which lie in Ln in terms of those whic...

The Exponential Map and Differential Equations on Real Lie Groups

Let G be a connected Lie group with Lie algebra g , expG : g −→ G the exponential map and E(G) its range. E(G) will denote the set of all n -fold products of elements of E(G). G is called exponential if E(G) = E(G) = G . Since most real (or complex) connected Lie groups are not exponential, it is of interest to know that the weaker conclusion E(G) = G is always true (Theorem 5.6). This result w...

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.