double derivations, higher double derivations and automatic continuity

Double Derivations, Higher Double Derivations and Automatic Continuity

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Automatic Continuity of Higher Derivations on JB*-Algebras

automatic continuity of higher derivations on jb*-algebras

Double derivations and Cyclic homology

We give a new construction of cyclic homology of an associative algebra A that does not involve Connes’ differential. Our approach is based on an extended version of the complex Ω q A, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any represe...

Double derivations of n-Lie algebras

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

δ-Double Derivations on C*-Algebras