Related papers: Type-I permanence

We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…

Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of…

We prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and connected, which is known, but is also commutative.

We prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $\omega$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…

In this paper we study the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup…

We present a systematic study of the structure of crossed products and fixed point algebras by compact group actions with the Rokhlin property on not necessarily unital C*-algebras. Our main technical result is the existence of an…

If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

We solve the long standing problem of classification of standard compact Clifford-Klein forms of homogeneous spaces of simple non-compact real Lie groups under the extra assumption that $G$, $H$, $L$ are simple and absolutely simple. Then…

Let $\mathbb{E}$ be the HNN-extension of a group $B$ with subgroups $H$ and $K$ associated according to an isomorphism $\varphi\colon H \to K$. Suppose that $H$ and $K$ are normal in $B$ and $(H \cap K)\varphi = H \cap K$. Under these…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

We study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We show that a locally compact c-minimal connected group is compact. Using a well-known theorem of Hall and Kulatilaka…

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…