Derivations and projections on Jordan triples: An introduction to nonassociative algebra, continuous cohomology, and quantum functional analysis

Derivations on ternary rings of operators

“…The first statement in (iii) follows from the fact that every finite dimensional semisimple Jordan triple system has only inner derivations. This result first appeared in [11,Chapter 11] (for an outline of a proof, see [14,Theorem 2.8,p. 136…”

Cohomology of Jordan triples via Lie algebras

“…A vector space M over the same scalar field is called a Jordan triple V -module (cf. [29]) if it is equipped with three mappings [25,Section 7]) . Extending the above product by linearity, we can define an action of V 0 on M 0 by…”

“…A vector space M over the same scalar field is called a Jordan triple V -module (cf. [29]) if it is equipped with three mappings For convenience, we shall omit the subscript…”

“…In the rest of this introduction, we give an overview of various cohomology theories, both classical and otherwise. (For a more detailed survey see [29].) In section 2, the definitions of Jordan triple module and Lie algebra module, as well as the Tits-Kantor-Koecher (TKK) construction are reviewed, basically following [5].…”