Related papers: Nonfree Actions of Countable Groups and their Char…

We provide a characterization of quotients of three-dimensional complex tori by finite groups that act freely in codimension one via a vanishing condition on the first and second orbifold Chern class. We also treat the case of actions free…

It is well known that if $G$ is a countable amenable group and $G \curvearrowright (Y, \nu)$ factors onto $G \curvearrowright (X, \mu)$, then the entropy of the first action must be greater than or equal to the entropy of the second action.…

This paper introduces the notion of fusion action system, an abstraction of the $p$-local data of a finite group acting on a finite set. Fusion action systems are closely connected with the theory of fusion systems; we detail the…

We will show the uniqueness of outer coactions of finite groups on the AFD factor of type II$_1$ along the arguments by Connes, Jones and Ocneanu. Namely, we construct the infinite tensor product type action, adopt it as the model action,…

We provide an elementary proof that subgroups of free groups are free via group actions.

A particularly easy, even if for long overlooked way is presented for defining globally arbitrary Lie group actions on smooth functions on Euclidean domains. This way is based on the appropriate use of the usual parametric representation of…

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…

These are introductory notes on some aspects of concentration of measure in the presence of an acting group and its links to Ramsey theory.

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

We describe the structure of the free actions of the Klein bottle group by orientation preserving homeomorphisms of the plane. This group is generated by two elements $a,b$, where the conjugate of $b$ by $a$ equals the inverse of $b$. The…

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

We define two complexes on which the group Aut$(F_n)$ acts freely. The homotopy groups of these are studied. They map to the K-groups of Z and are themselves a sort of pre-K-theory.

An analogue of Krein's extension theorem is proved for operator-valued positive definite functions on free groups. The proof gives also the parametrization of all extensions by means of a generalized type of Szego parameters. One singles…

We study hereditary properties of the class of countable groups admitting an amenable, transitive and faithful action on a countable set. We consider mainly the case of amalgamated free products, and we show in particular that the double of…

In this article we generalize the results of the previous article with the same title [arXiv:0901.3308] for the case of an arbitrariy linear representation and non-normal stationary subgroup.

This is an expository paper aimed to outline the current situation with problems related with the occurrence of eigenvalue $1$ of elements in linear groups and group representations.

We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.

We investigate actions of cyclic groups on polynomial rings with two variables, and the minimal free resolution of the corresponding invariant ring. In particular, we fully classify several cases, including the case the defining ideal has…

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…