This note gives an account of the algebraic construction of symbolic covers and representations of ergodic automorphisms of compact abelian groups. For expansive toral automorphisms this subject was initiated by A.M. Vershik.

Using McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.

In this paper, the problem formulated in [8] is solved. We prove, that the group of automorphisms of the category of free associative algebras is generated by semi-inner and mirror automorphisms.

We extend Forester’s rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups). Let T be a simplicial tree with a cocompact action of a group G (i.e. the BassSerre tree associated to a decompos...

Let Aut(X, B) be the group of all Borel automorphisms of a standard Borel space (X, B). We study topological properties of Aut(X, B) with respect to the uniform and weak topologies, τ and p, defined in [BDK1]. It is proved that the class of smooth automorphisms is dense in (Aut(X, B), p). Let Ctbl(X) denote the group of Borel automorphisms with countable support. It is shown that the topologica...

After discussing some basic facts about generalized module maps, we use the representation theory of the algebra Ba(E) of adjointable operators on a Hilbert B–module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal BE of E in B. We determine the kernel of the canonical ...

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of ∗-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covaria...

The affine group schemes of automorphisms the multilinear r -fold cross products on finite-dimensional vectors spaces over fields characteristic not two are determined. Gradings by abelian groups these structures, that correspond to morphisms from diagonalizable into automorphisms, completely classified, up isomorphism.