Automorphisms and Higher Derivations of Incidence Algebras

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Derivations and Automorphisms of Certain Operator Algebras

Prime Higher Derivations on Algebras

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

A Note on Automorphisms and Derivations of Lie Algebras

In a recent paper Borel and Serre proved the theorem: If 8 is a Lie algebra of characteristic 0 and 8 has an automorphism of prime period without fixed points f^O, then 8 is nilpotent.1 In this note we give a proof valid also for characteristic p^O. By the same method we can prove several other similar results on automorphisms and derivations. Our method is based on decompositions of the Lie al...