CYCLOMORPHY

DAN-VIRGIL VOICULESCU

Abstract. A main result is that, roughly, a dense set of the infinitesimal tracepreserving deformations of a semicircular system s_{1}, …, s_{n} arise from one-parameter groups of automorphisms of the free-group factor L(F (n)) generated by s_{1}, …, s_{n}. More generally the paper studies cyclic gradients in von Neumann algebras, Lie algebras of noncommutative trace-preserving vector fields and the class of cyclomorphic maps which preserve the orthogonals of spaces of cyclic gradients.