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.

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph C∗-algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

We extend the notion of the canonical extension of automorphisms of type III factors to the case of endomorphisms with finite statistical dimensions. Following the automorphism case, we introduce two notions for endomorphisms of type III factors: modular endomorphisms and Connes-Takesaki modules. Several applications to compact groups of automorphisms and subfactors of type III factors are give...

This article describes the use of permutation representations to obtain a partial solution to the Extensible Automorphisms Problem. It introduces a notion of permutation-extensibility and proves the equivalence of this notion with the notion of being subgroup-conjugating. 1. The problem we want to solve 1.1. Three big problems. A quick recall of three definitions: Definition. (1) An automorphis...

This article gives the proof of results announced in [Bla07a] and some description of automorphisms of rational surfaces. Given a finite abelian subgroup of the Cremona group of the plane, we give a way to decide whether this one is birationally conjugate to a group of automorphisms of a minimal surface. In particular, we prove that a finite cyclic group of birational transformations of the pla...