Cohomologies of Reynolds operators on <i>n</i>-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.

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 ...

Family of operators and their Lie algebras

Lie Algebras of Differential Operators and Lie-Algebraic Potentials

An explicit characterisation of all second order differential operators on the line which can be written as bilinear combinations of the generators of a linitedimensional Lie algebra of first order differential operators is found, solving a problem arising in the Lie-algebraic approach to scattering theory and molecular dynamics. One-dimensional potentials corresponding to these Lie algebras ar...

Representations of Lie Algebras by Normal Operators

Recently I. E. Segal [2] has proposed a study of the unitary representations of a complex semisimple Lie group G by studying "analytic" holomorphic representations of G by normal operators. To this end he proved that every unitary representation U of G may be written U(g)=R(g)R(g~1)* (gEG) where R is an analytic holomorphic representation of G by normal operators such that if R(gi) and R(g2) ar...