C. R. E. Raja
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View article: IRS on orbits and the case of $SL(2, \mathbb{R} ) \ltimes \mathbb{R} ^2$
IRS on orbits and the case of $SL(2, \mathbb{R} ) \ltimes \mathbb{R} ^2$ Open
Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…
View article: BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS
BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS Open
We consider conjugacy classes in a locally compact group G that support finite G -invariant measures. If G is a property (M) extension of an abelian group, in particular, if G is a metabelian group, then any such conjugacy class is relativ…
View article: Group actions and power maps for groups over non-Archimedean local fields
Group actions and power maps for groups over non-Archimedean local fields Open
We consider linear groups and Lie groups over a non-Archimedean local field $\mathbb F$ for which the power map $x\mapsto x^k$ has a dense image or it is surjective. We prove that the group of $\mathbb F$-points of such algebraic groups is…
View article: Peer Review #2 of "Pangenomic type III effector database of the plant pathogenic Ralstonia spp. (v0.1)"
Peer Review #2 of "Pangenomic type III effector database of the plant pathogenic Ralstonia spp. (v0.1)" Open
Background.The bacterial plant pathogenic Ralstonia species belong to the beta-proteobacteria class and are soil-borne pathogens causing vascular bacterial wilt disease, affecting a wide range of plant hosts.These bacteria form a heterogen…
View article: 2-step nilpotent Lie groups and hyperbolic automorphisms
2-step nilpotent Lie groups and hyperbolic automorphisms Open
A connected Lie group admitting an expansive automorphism is known to be nilpotent, but all nilpotent Lie groups do not admit expansive automorphism. In this article, we find sufficient conditions for a class of nilpotent Lie groups to adm…
View article: Some properties of distal actions on locally compact groups
Some properties of distal actions on locally compact groups Open
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 obtain a decomposition for contraction group…
View article: Expansive automorphisms of totally disconnected, locally compact groups
Expansive automorphisms of totally disconnected, locally compact groups Open
We study topological automorphisms α of a totally disconnected, locally compact group G which are expansive in the sense that ⋂ n ∈ ℤ α n ( U ) = { 1 } $\bigcap_{n\in{\mathbb{Z}}}\alpha^{n}(U)=\{1\}$ for some identity n…