Cyclomorphy

الأصل · EN

A main result is that, roughly, a dense set of the infinitesimal trace-preserving deformations of a semicircular system s₁,..., sₙ arise from one-parameter groups of automorphisms of the free-group factor L(F(n)) generated by s₁,..., sₙ. 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.